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 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
A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified ...A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multioutput kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well.展开更多
Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower tri...Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower triangular matrix is derived from Cholesky decomposition of a reference spectrum matrix. The diagonal elements of the lower triangular matrix （DELTM） may become negative. These negative values have no meaning in physical significance and can cause divergence of auto-power spectrum control. A proportional root mean square control algorithm （PRMSCA） provides another method to avoid the divergence caused by negative values of DELTM, but PRMSCA cannot control the cross-power spectrum. A new control algorithm named matrix power control algorithm （MPCA） is proposed in the paper. MPCA can guarantee that DELTM is always positive in the auto-power spectrum control. MPCA can also control the cross-power spectrum. After these three control algorithms are analyzed, three-input three-output random vibration control tests are implemented on a three-axis vibration shaker. The results show the validity of the proposed MPCA.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
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 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 Priority Academic Program Development of Jiangsu Higher Education Institutionsthe Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_0234)
文摘A control method for Multi-Input Multi-Output（MIMO） non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multioutput kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well.
基金National Natural Science Foundation of China （10972104） The Fundamental Research Funds for NUAA（NS2010007）
文摘Both auto-power spectrum and cross-power spectrum need to be controlled in multi-input multi-output （MIMO） random vibration test. During the control process with the difference control algorithm （DCA）, a lower triangular matrix is derived from Cholesky decomposition of a reference spectrum matrix. The diagonal elements of the lower triangular matrix （DELTM） may become negative. These negative values have no meaning in physical significance and can cause divergence of auto-power spectrum control. A proportional root mean square control algorithm （PRMSCA） provides another method to avoid the divergence caused by negative values of DELTM, but PRMSCA cannot control the cross-power spectrum. A new control algorithm named matrix power control algorithm （MPCA） is proposed in the paper. MPCA can guarantee that DELTM is always positive in the auto-power spectrum control. MPCA can also control the cross-power spectrum. After these three control algorithms are analyzed, three-input three-output random vibration control tests are implemented on a three-axis vibration shaker. The results show the validity of the proposed MPCA.
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.
