This work presents a stochastic Chebyshev-Picard iteration method to efficiently solve nonlinear differential equations with random inputs.If the nonlinear problem involves uncertainty,we need to characterize the unce...This work presents a stochastic Chebyshev-Picard iteration method to efficiently solve nonlinear differential equations with random inputs.If the nonlinear problem involves uncertainty,we need to characterize the uncer-tainty by using a few random variables.The nonlinear stochastic problems require solving the nonlinear system for a large number of samples in the stochastic space to quantify the statistics of the system of response and explore the uncertainty quantification.The computational cost is very expensive.To overcome the difficulty,a low rank approximation is introduced to the solution of the corresponding nonlinear problem and admits a variable-separation form in terms of stochastic basis functions and deterministic basis functions.No it-eration is performed at each enrichment step.These basis functions are model-oriented and involve offline computation.To efficiently identify the stochastic basis functions,we utilize the greedy algorithm to select some optimal sam-ples.Then the modified Chebyshev-Picard iteration method is used to solve the nonlinear system at the selected optimal samples,the solutions of which are used to train the deterministic basis functions.With the deterministic basis functions,we can obtain the corresponding stochastic basis functions by solv-ing linear differential systems.The computation of the stochastic Chebyshev-Picard method decomposes into an offline phase and an online phase.This is very desirable for scientific computation.Several examples are presented to illustrate the efficacy of the proposed method for different nonlinear differential equations.展开更多
For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the ...For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the fact that the fuzziness of the output response is determined by that of the input variable, the presented measure system defines the importance measures which evaluate the effect of the fuzzy input variable. And for the random input variable, the importance measure system analyzes its effect from two aspects, i.e. its effect on the central distribution position and that on the fuzzy degree of the membership function of the output response. Taking the effects of the two kinds of input variables on the first moment and second one of the output response into account, the definitions of the importance measures of the input variables are given and their engineering significations are demonstrated. Combining with the advantages of the point estimates of Zhao and Ono, a solution of the proposed importance measures is provided. Several examples show that the proposed measure system is comprehensive and reasonable, and the proposed solution can improve computational efficiency considerably with acceptable precision.展开更多
This paper addresses the direction of arrival （DOA） estimation problem for the co-located multiple-input multiple- output （MIMO） radar with random arrays. The spatially distributed sparsity of the targets in the b...This paper addresses the direction of arrival （DOA） estimation problem for the co-located multiple-input multiple- output （MIMO） radar with random arrays. The spatially distributed sparsity of the targets in the background makes com- pressive sensing （CS） desirable for DOA estimation. A spatial CS framework is presented, which links the DOA estimation problem to support recovery from a known over-complete dictionary. A modified statistical model is developed to ac- curately represent the intra-block correlation of the received signal. A structural sparsity Bayesian learning algorithm is proposed for the sparse recovery problem. The proposed algorithm, which exploits intra-signal correlation, is capable being applied to limited data support and low signal-to-noise ratio （SNR） scene. Furthermore, the proposed algorithm has less computation load compared to the classical Bayesian algorithm. Simulation results show that the proposed algorithm has a more accurate DOA estimation than the traditional multiple signal classification （MUSIC） algorithm and other CS recovery algorithms.展开更多
超大规模多输入多输出(Extra-Large Scale Multiple-Input Multiple-Output,XL-MIMO)是未来的第六代移动通信(The 6th Generation Mobile Communication Technology,6G)关键技术之一,但是由于XL-MIMO系统采用了超大规模天线阵列,其信号...超大规模多输入多输出(Extra-Large Scale Multiple-Input Multiple-Output,XL-MIMO)是未来的第六代移动通信(The 6th Generation Mobile Communication Technology,6G)关键技术之一,但是由于XL-MIMO系统采用了超大规模天线阵列,其信号处理需求非常庞大,增加了计算复杂度。这对信号的检测算法有了更高的要求,由此对XL-MIMO系统中低复杂度算法进行研究是十分重要的。首先介绍了XL-MIMO系统信道模型,然后引入了预编码技术,将随机Kaczmarz算法和传统的MMSE算法在完美非平稳信道的归一化传输功率的误码率情况、用户数量复杂度情况、天线数量复杂度情况进行了仿真分析与比较。结果表明随机Kaczmarz算法具有更低的计算复杂度,并且是一种可以准确实现的快速算法。展开更多
Floyd提出的随机早丢弃(RED,random early detection)是基于传统的泊松(Possion)模型,不适应网络流量普遍呈现自相似性的特点。基于此目的,提出了一种新的RED算法——Hurst加权随机早检测算法(HWRED,Hurst weighted random early detect...Floyd提出的随机早丢弃(RED,random early detection)是基于传统的泊松(Possion)模型,不适应网络流量普遍呈现自相似性的特点。基于此目的,提出了一种新的RED算法——Hurst加权随机早检测算法(HWRED,Hurst weighted random early detection)。新算法能够根据输入流量的自相似系数Hurst,调整RED算法参数。仿真结果表明,新算法提高了队列长度的稳定性,减少了丟包率、排队时延和排队抖动,提高了网络的链路利用率。展开更多
基金supported by the National Natural Science Foundation of China (Grant No.12101217)by the China Postdoctoral Science Foundation (Grant No.2022M713875)by the Natural Science Foundation of Hunan Province (Grant No.2022J40113).
文摘This work presents a stochastic Chebyshev-Picard iteration method to efficiently solve nonlinear differential equations with random inputs.If the nonlinear problem involves uncertainty,we need to characterize the uncer-tainty by using a few random variables.The nonlinear stochastic problems require solving the nonlinear system for a large number of samples in the stochastic space to quantify the statistics of the system of response and explore the uncertainty quantification.The computational cost is very expensive.To overcome the difficulty,a low rank approximation is introduced to the solution of the corresponding nonlinear problem and admits a variable-separation form in terms of stochastic basis functions and deterministic basis functions.No it-eration is performed at each enrichment step.These basis functions are model-oriented and involve offline computation.To efficiently identify the stochastic basis functions,we utilize the greedy algorithm to select some optimal sam-ples.Then the modified Chebyshev-Picard iteration method is used to solve the nonlinear system at the selected optimal samples,the solutions of which are used to train the deterministic basis functions.With the deterministic basis functions,we can obtain the corresponding stochastic basis functions by solv-ing linear differential systems.The computation of the stochastic Chebyshev-Picard method decomposes into an offline phase and an online phase.This is very desirable for scientific computation.Several examples are presented to illustrate the efficacy of the proposed method for different nonlinear differential equations.
基金supported by the National Natural Science Foundation of China (Grant No. NSFC 50875213)
文摘For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the fact that the fuzziness of the output response is determined by that of the input variable, the presented measure system defines the importance measures which evaluate the effect of the fuzzy input variable. And for the random input variable, the importance measure system analyzes its effect from two aspects, i.e. its effect on the central distribution position and that on the fuzzy degree of the membership function of the output response. Taking the effects of the two kinds of input variables on the first moment and second one of the output response into account, the definitions of the importance measures of the input variables are given and their engineering significations are demonstrated. Combining with the advantages of the point estimates of Zhao and Ono, a solution of the proposed importance measures is provided. Several examples show that the proposed measure system is comprehensive and reasonable, and the proposed solution can improve computational efficiency considerably with acceptable precision.
基金supported by the National Natural Science Foundation of China(Grant Nos.61071163,61271327,and 61471191)the Funding for Outstanding Doctoral Dissertation in Nanjing University of Aeronautics and Astronautics,China(Grant No.BCXJ14-08)+2 种基金the Funding of Innovation Program for Graduate Education of Jiangsu Province,China(Grant No.KYLX 0277)the Fundamental Research Funds for the Central Universities,China(Grant No.3082015NP2015504)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PADA),China
文摘This paper addresses the direction of arrival （DOA） estimation problem for the co-located multiple-input multiple- output （MIMO） radar with random arrays. The spatially distributed sparsity of the targets in the background makes com- pressive sensing （CS） desirable for DOA estimation. A spatial CS framework is presented, which links the DOA estimation problem to support recovery from a known over-complete dictionary. A modified statistical model is developed to ac- curately represent the intra-block correlation of the received signal. A structural sparsity Bayesian learning algorithm is proposed for the sparse recovery problem. The proposed algorithm, which exploits intra-signal correlation, is capable being applied to limited data support and low signal-to-noise ratio （SNR） scene. Furthermore, the proposed algorithm has less computation load compared to the classical Bayesian algorithm. Simulation results show that the proposed algorithm has a more accurate DOA estimation than the traditional multiple signal classification （MUSIC） algorithm and other CS recovery algorithms.
文摘超大规模多输入多输出(Extra-Large Scale Multiple-Input Multiple-Output,XL-MIMO)是未来的第六代移动通信(The 6th Generation Mobile Communication Technology,6G)关键技术之一,但是由于XL-MIMO系统采用了超大规模天线阵列,其信号处理需求非常庞大,增加了计算复杂度。这对信号的检测算法有了更高的要求,由此对XL-MIMO系统中低复杂度算法进行研究是十分重要的。首先介绍了XL-MIMO系统信道模型,然后引入了预编码技术,将随机Kaczmarz算法和传统的MMSE算法在完美非平稳信道的归一化传输功率的误码率情况、用户数量复杂度情况、天线数量复杂度情况进行了仿真分析与比较。结果表明随机Kaczmarz算法具有更低的计算复杂度,并且是一种可以准确实现的快速算法。
文摘Floyd提出的随机早丢弃(RED,random early detection)是基于传统的泊松(Possion)模型,不适应网络流量普遍呈现自相似性的特点。基于此目的,提出了一种新的RED算法——Hurst加权随机早检测算法(HWRED,Hurst weighted random early detection)。新算法能够根据输入流量的自相似系数Hurst,调整RED算法参数。仿真结果表明,新算法提高了队列长度的稳定性,减少了丟包率、排队时延和排队抖动,提高了网络的链路利用率。
