The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resona...The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.展开更多
面向对象程序整体结构及其特性的逆向分析和可视化在软件维护、软件重用等过程中起着重要作用。现有的逆向工程工具尽管可以通过对程序代码的静态分析自动获取类模型,但是在自动布图方面仍存在一些明显的问题,特别是难以直观展现类之间...面向对象程序整体结构及其特性的逆向分析和可视化在软件维护、软件重用等过程中起着重要作用。现有的逆向工程工具尽管可以通过对程序代码的静态分析自动获取类模型,但是在自动布图方面仍存在一些明显的问题,特别是难以直观展现类之间的耦合性、聚集效应等程序整体结构的重要特性,从而影响其实际应用。Force-Directed Layout算法能够自然展现复杂结构的耦合关系和聚集现象,因此,将其应用于类图的逆向生成,使其在充分展示程序整体结构的同时,清晰展现类之间的耦合性和聚集效应等结构特征,为软件结构演化分析、缺陷分布分析等提供辅助支持。据此,开发了软件分析与测试工具系列QESat的子工具——基于拉力算法的类图可视化工具QESat/FCD(Quality Easy-Software Analysis and Testing Tools:Force-Directed Class Diagram),通过实例展示了其在大型类图结构特性方面的展现效果。展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 12072118)the Natural Science Funds for Distinguished Young Scholar of the Fujian Province, China (Grant No. 2021J06024)the Project for Youth Innovation Fund of Xiamen, China (Grant No. 3502Z20206005)。
文摘The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.
文摘面向对象程序整体结构及其特性的逆向分析和可视化在软件维护、软件重用等过程中起着重要作用。现有的逆向工程工具尽管可以通过对程序代码的静态分析自动获取类模型,但是在自动布图方面仍存在一些明显的问题,特别是难以直观展现类之间的耦合性、聚集效应等程序整体结构的重要特性,从而影响其实际应用。Force-Directed Layout算法能够自然展现复杂结构的耦合关系和聚集现象,因此,将其应用于类图的逆向生成,使其在充分展示程序整体结构的同时,清晰展现类之间的耦合性和聚集效应等结构特征,为软件结构演化分析、缺陷分布分析等提供辅助支持。据此,开发了软件分析与测试工具系列QESat的子工具——基于拉力算法的类图可视化工具QESat/FCD(Quality Easy-Software Analysis and Testing Tools:Force-Directed Class Diagram),通过实例展示了其在大型类图结构特性方面的展现效果。
