An Improved Typhoon Simulation Method Based On Latin Hypercube Sampling Method

In order to further improve the prediction accuracy of typhoon simulation method for extreme wind speed in typhoon prone areas, an improved typhoon simulation method is proposed by introducing the Latin hypercube sampling method into the traditional typhoon simulation method. In this paper, the improved typhoon simulation method is first given a detailed introduction. Then, this method is applied to the prediction of extreme wind speeds under various return periods in Hong Kong. To validate this method, two aspects of analysis is carried out, including correlation analysis among typhoon key parameters and prediction of extreme wind speeds under various return periods. The results show that the correlation coefficients among typhoon key parameters can be maintained satisfactorily with this improved typhoon simulation method. Compared with the traditional typhoon simulation method, extreme wind speeds under various return periods obtained with this improved typhoon simulation method are much closer to the results obtained with historical typhoon wind data.

Explorative gradient method for active drag reduction of the fluidic pinball and slanted Ahmed body

We address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding suboptimal local minima. This challenge is addressed by a new optimizer, called the explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hypercube sampling iteration. Thus, the convergence rate of a gradient based method is guaranteed while, at the same time, better minima are explored. For an analytical multi-modal test function, EGM is shown to significantly outperform the downhill simplex method, the random restart simplex, Latin hypercube sampling, Monte Carlo sampling and the genetic algorithm. EGM is applied to minimize the net drag power of the two-dimensional fluidic pinball benchmark with three cylinder rotations as actuation parameters. The net drag power is reduced by 29 % employing direct numerical simulations at a Reynolds number of $100$ based on the cylinder diameter. This optimal actuation leads to 52 % drag reduction employing Coanda forcing for boat tailing and partial stabilization of vortex shedding. The price is an actuation energy corresponding to 23 % of the unforced parasitic drag power. EGM is also used to minimize drag of the $35^\circ$ slanted Ahmed body employing distributed steady blowing with 10 inputs. 17 % drag reduction are achieved using Reynolds-averaged Navier–Stokes simulations at the Reynolds number $Re_H=1.9 \times 10^5$ based on the height of the Ahmed body. The wake is controlled with seven local jet-slot actuators at all trailing edges. Symmetric operation corresponds to five independent actuator groups at top, middle, bottom, top sides and bottom sides. Each slot actuator produces a uniform jet with the velocity and angle as free parameters, yielding 10 actuation parameters as free inputs. The optimal actuation emulates boat tailing by inward-directed blowing with velocities which are comparable to the oncoming velocity. We expect that EGM will be employed as efficient optimizer in many future active flow control plants as alternative or augmentation to pure gradient search or explorative methods.

Penetration Depth Prediction of Infinity Shaped Laser Scanning Welding Based on Latin Hypercube Sampling and the Neuroevolution of Augmenting Topologies

This paper builds an infinity shaped (“∞”-shaped) laser scanning welding test platform based on a self-developed motion controller and galvanometer scanner control gateway, takes the autogenous bead-on-plate welding of 304SS with 3 mm thick specimens as the experimental objects, designs the experimental parameters by the Latin hypercube sampling method for obtaining different penetration depth welded joints, and presents a methodology based on the neuroevolution of augmenting topologies for predicting the penetration depth of “∞”-shaped laser scanning welding. Laser power, welding speed, scanning frequency, and scanning amplitude are set as the input parameters of the model, and welding depth (WD) as the output parameter of the model. The model can accurately reflect the nonlinear relationship between the main welding parameters and WD by validation. Moreover, the normalized root mean square error (NRMSE) of the welding depth is about 6.2%. On the whole, the proposed methodology and model can be employed for guiding the actual work in the main process parameters’ preliminary selection and lay the foundation for the study of penetration morphology control of “∞”-shaped laser scanning welding.

Transversals, Near Transversals, and Diagonals in Iterated Groups and Quasigroups

Given a binary quasigroup $G$ of order $n$, a $d$-iterated quasigroup $G[d]$ is the $(d+1)$-ary quasigroup equal to the $d$-times composition of $G$ with itself. The Cayley table of every $d$-ary quasigroup is a $d$-dimensional latin hypercube. Transversals and diagonals in multiary quasigroups are defined so as to coincide with those in the corresponding latin hypercube. We prove that if a group $G$ of order $n$ satisfies the Hall–Paige condition, then the number of transversals in $G[d]$ is equal to $ \frac{n!}{ |G'| n^{n-1}} \cdot n!^{d} (1 + o(1))$ for large $d$, where $G'$ is the commutator subgroup of $G$. For a general quasigroup $G$, we obtain similar estimations on the numbers of transversals and near transversals in $G[d]$ and develop a method for counting diagonals of other types in iterated quasigroups.