Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian ...Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems.展开更多
In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-so...In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P. Aubin et al. are generalized and improved.展开更多
A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed proba...A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.展开更多
A differential evolution based methodology is introduced for the solution of elliptic partial differential equations (PDEs) with Dirichlet and/or Neumann boundary conditions. The solutions evolve over bounded domains ...A differential evolution based methodology is introduced for the solution of elliptic partial differential equations (PDEs) with Dirichlet and/or Neumann boundary conditions. The solutions evolve over bounded domains throughout the interior nodes by minimization of nodal deviations among the population. The elliptic PDEs are replaced by the corresponding system of finite difference approximation, yielding an expression for nodal residues. The global residue is declared as the root-mean-square value of the nodal residues and taken as the cost function. The standard differential evolution is then used for the solution of elliptic PDEs by conversion to a minimization problem of the global residue. A set of benchmark problems consisting of both linear and nonlinear elliptic PDEs has been considered for validation, proving the effectiveness of the proposed algorithm. To demonstrate its robustness, sensitivity analysis has been carried out for various differential evolution operators and parameters. Comparison of the differential evolution based computed nodal values with the corresponding data obtained using the exact analytical expressions shows the accuracy and convergence of the proposed methodology.展开更多
科技行业的快速发展带来信息量的暴增,各行各业都需要收集和应用大量的数据,海量数据在发挥价值的同时,给数据安全领域带来了史无前例的挑战。关系型数据库作为数据的底层存储载体之一,其存储的数据规模大、数据内容丰富、数据隐私度高...科技行业的快速发展带来信息量的暴增,各行各业都需要收集和应用大量的数据,海量数据在发挥价值的同时,给数据安全领域带来了史无前例的挑战。关系型数据库作为数据的底层存储载体之一,其存储的数据规模大、数据内容丰富、数据隐私度高。数据库的数据一旦泄露将会造成巨大的损失,保护数据库的所有权,确认数据的归属刻不容缓。对于现有的数据库水印技术来说,提高水印嵌入容量和减小数据失真之间存在固有矛盾问题,为了缓解此问题且进一步提高水印的鲁棒性,提出了一种基于动态差分扩展的强鲁棒数据库水印算法。该算法选取QR码作为水印,利用经过Haar小波变换的图像低频部分进行奇异值分解(SVD,singular value decomposition),提取部分特征值,用取余后的特征值作为待嵌入的水印序列,使得相同长度的水印序列包含更多信息,缩短了嵌入水印的长度。该算法结合自适应差分进化算法和最小差值算法选择最佳嵌入属性位,以缓解传统差分扩展技术在嵌入水印时计算效率低、数据失真大、鲁棒性差的问题,提高水印嵌入容量的同时减少了数据的失真。实验结果表明,该算法保证高水印嵌入率的同时数据失真较低,能够抵御多种攻击,具有良好的鲁棒性,追踪溯源的能力强,且与现有的算法对比优势明显,在数据安全领域具有广阔的应用前景。展开更多
基金The supports of the National Natural Science Foundation of China(Grant Nos.51725804 and U1711264)the Research Fund for State Key Laboratories of Ministry of Science and Technology of China(SLDRCE19-B-23)the Shanghai Post-Doctoral Excellence Program(2022558)。
文摘Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems.
文摘In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P. Aubin et al. are generalized and improved.
基金National Natural Science Foundation of China for Innovative Research Groups Under Grant No. 50321803 National Natural Science Foundation of China for Young Scholars Under Grant No. 10402030
文摘A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.
文摘A differential evolution based methodology is introduced for the solution of elliptic partial differential equations (PDEs) with Dirichlet and/or Neumann boundary conditions. The solutions evolve over bounded domains throughout the interior nodes by minimization of nodal deviations among the population. The elliptic PDEs are replaced by the corresponding system of finite difference approximation, yielding an expression for nodal residues. The global residue is declared as the root-mean-square value of the nodal residues and taken as the cost function. The standard differential evolution is then used for the solution of elliptic PDEs by conversion to a minimization problem of the global residue. A set of benchmark problems consisting of both linear and nonlinear elliptic PDEs has been considered for validation, proving the effectiveness of the proposed algorithm. To demonstrate its robustness, sensitivity analysis has been carried out for various differential evolution operators and parameters. Comparison of the differential evolution based computed nodal values with the corresponding data obtained using the exact analytical expressions shows the accuracy and convergence of the proposed methodology.
文摘科技行业的快速发展带来信息量的暴增,各行各业都需要收集和应用大量的数据,海量数据在发挥价值的同时,给数据安全领域带来了史无前例的挑战。关系型数据库作为数据的底层存储载体之一,其存储的数据规模大、数据内容丰富、数据隐私度高。数据库的数据一旦泄露将会造成巨大的损失,保护数据库的所有权,确认数据的归属刻不容缓。对于现有的数据库水印技术来说,提高水印嵌入容量和减小数据失真之间存在固有矛盾问题,为了缓解此问题且进一步提高水印的鲁棒性,提出了一种基于动态差分扩展的强鲁棒数据库水印算法。该算法选取QR码作为水印,利用经过Haar小波变换的图像低频部分进行奇异值分解(SVD,singular value decomposition),提取部分特征值,用取余后的特征值作为待嵌入的水印序列,使得相同长度的水印序列包含更多信息,缩短了嵌入水印的长度。该算法结合自适应差分进化算法和最小差值算法选择最佳嵌入属性位,以缓解传统差分扩展技术在嵌入水印时计算效率低、数据失真大、鲁棒性差的问题,提高水印嵌入容量的同时减少了数据的失真。实验结果表明,该算法保证高水印嵌入率的同时数据失真较低,能够抵御多种攻击,具有良好的鲁棒性,追踪溯源的能力强,且与现有的算法对比优势明显,在数据安全领域具有广阔的应用前景。
文摘为了优化气隙磁通密度波形的幅值与正弦畸变率2个关键指标,提出了一种基于Kriging模型与差分进化算法(differential evolution algorithm,DEA)相结合的多目标优化方法。首先,通过对飞轮储能用永磁同步电机(permanent magnet synchronous motor for flywheel energy storage,FPMSM)有限元模型进行拉丁超立方体采样(Latin hypercube sampling,LHS),取得样本数据,并引入Kriging算法建立对应的替代模型;其次,利用DEA对影响气隙磁通密度波形的关键结构参数进行全局优化,给出Pareto最优解;最后,对Pareto最优解集的3种优化方案与原始方案进行对比分析和有限元验证。结果表明,所提FPMSM气隙磁通密度波形多目标优化方法能够使气隙磁通密度波形在幅值提高的同时,正弦畸变率显著降低。
