In this paper we devote ourselves to extending Berman’s sojourn time method,which is thoroughly described in[1-3],to investigate the tail asymptotics of the extrema of a Gaussian random field over[0,T]^(d) with T∈(0...In this paper we devote ourselves to extending Berman’s sojourn time method,which is thoroughly described in[1-3],to investigate the tail asymptotics of the extrema of a Gaussian random field over[0,T]^(d) with T∈(0,∞).展开更多
A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Ran...A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.展开更多
In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question ...In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.展开更多
The collective behavior of a ring of coupled identical van der Pol oscillators is numerically studied in this work. Constant, gaussian and random distributions of the coupling parameter along the ring are considered. ...The collective behavior of a ring of coupled identical van der Pol oscillators is numerically studied in this work. Constant, gaussian and random distributions of the coupling parameter along the ring are considered. Three values of the oscillators constant are assumed in order to cover from quasilinear to nonlinear dynamic performance. Single and multiple coupled frequencies are obtained using power spectra of the long term time series. Phase portraits are obtained from numerical simulations, and the coupled behavior is analyzed, compared and discussed.展开更多
Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the...Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.展开更多
针对无人机路径规划求解计算量大、难收敛等问题,提出了一种基于全粒子推动野马算法的路径规划方法。建立三维环境模型与路径代价模型,将路径规划问题转化为多维函数优化问题;采用一种自适应邻域搜索策略,改善算法的开发能力;利用高斯...针对无人机路径规划求解计算量大、难收敛等问题,提出了一种基于全粒子推动野马算法的路径规划方法。建立三维环境模型与路径代价模型,将路径规划问题转化为多维函数优化问题;采用一种自适应邻域搜索策略,改善算法的开发能力;利用高斯随机游走策略对个体的历史最优位置进行回溯搜索,改善算法的探索能力;考虑到自适应策略对初始种群多样性敏感的问题,结合Tent混沌映射初始化种群,提高算法的鲁棒性以及全局寻优能力;将提出的改进算法在13个经典测试函数中进行性能验证,并移植于无人机三维路径规划问题中。在30峰、40峰、50峰的环境模型下进行测试,与遗传算法、粒子群算法、SRM-PSO(self-regulating and self-perception particle swarm optimization with mutation mechanism)算法以及野马算法对比,全粒子推动野马算法皆取得最短平均路径,且在所有测试中都找到满足约束、无碰的路径。仿真结果证明,在复杂环境下全粒子推动野马算法具有优秀的全局寻优能力以及较好的鲁棒性。展开更多
基金partially supported by National Natural Science Foundation of China(11701070,71871046)Ronglian Scholarship Fund.
文摘In this paper we devote ourselves to extending Berman’s sojourn time method,which is thoroughly described in[1-3],to investigate the tail asymptotics of the extrema of a Gaussian random field over[0,T]^(d) with T∈(0,∞).
文摘A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.
基金This work is funded by National Natural Science Foundation of China
文摘In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.
文摘The collective behavior of a ring of coupled identical van der Pol oscillators is numerically studied in this work. Constant, gaussian and random distributions of the coupling parameter along the ring are considered. Three values of the oscillators constant are assumed in order to cover from quasilinear to nonlinear dynamic performance. Single and multiple coupled frequencies are obtained using power spectra of the long term time series. Phase portraits are obtained from numerical simulations, and the coupled behavior is analyzed, compared and discussed.
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(12ZB082)the Scientific research cultivation project of Sichuan University of Science&Engineering(2013PY07)+1 种基金the Scientific Research Fund of Shanghai University of Finance and Economics(2017110080)the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing(2018QZJ01)
文摘Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x → ∞.
文摘针对无人机路径规划求解计算量大、难收敛等问题,提出了一种基于全粒子推动野马算法的路径规划方法。建立三维环境模型与路径代价模型,将路径规划问题转化为多维函数优化问题;采用一种自适应邻域搜索策略,改善算法的开发能力;利用高斯随机游走策略对个体的历史最优位置进行回溯搜索,改善算法的探索能力;考虑到自适应策略对初始种群多样性敏感的问题,结合Tent混沌映射初始化种群,提高算法的鲁棒性以及全局寻优能力;将提出的改进算法在13个经典测试函数中进行性能验证,并移植于无人机三维路径规划问题中。在30峰、40峰、50峰的环境模型下进行测试,与遗传算法、粒子群算法、SRM-PSO(self-regulating and self-perception particle swarm optimization with mutation mechanism)算法以及野马算法对比,全粒子推动野马算法皆取得最短平均路径,且在所有测试中都找到满足约束、无碰的路径。仿真结果证明,在复杂环境下全粒子推动野马算法具有优秀的全局寻优能力以及较好的鲁棒性。
