The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） r...The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method（NIPCM） that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.展开更多
In this paper the development of reactive software is transformed into a control problem, and the supervisory control theory for discrete event dynamic systems is suggested to solve this control problem. The operating...In this paper the development of reactive software is transformed into a control problem, and the supervisory control theory for discrete event dynamic systems is suggested to solve this control problem. The operating environment under consideration is viewed as a controlled plant, the software under development as the corresponding controller, and the software requirements as the corresponding control objective. This idea leads to a constructive approach of software design, which ensures properties required a priori of the software under development. In this way the validation of the software under development is reduced to the validation of properties independent of implementation process. We reveal the inconsistence in using the concept of reachability to specify software requirements and clarify six different definitions of reachability. Two different definitions of invariance for specifying software requirements are also clarified. We then show how to synthesize the required controller or obtain software design solutions if the underlying software requirements are specified by several new combinations of reachability and invariance. The topic of this paper falls into the scope of software cybernetics that explores the interplay between software and control.展开更多
基金supported by the National Natural Science Foundation of China (No. 51105034)the Doctoral Thesis Build Project of Beijing 2012 (China)
文摘The classic polynomial chaos method（PCM）, characterized as an intrusive methodology,has been applied to uncertainty propagation（UP） in many dynamic systems. However, the intrusive polynomial chaos method（IPCM） requires tedious modification of the governing equations, which might introduce errors and can be impractical. Alternative to IPCM, the non-intrusive polynomial chaos method（NIPCM） that avoids such modifications has been developed. In spite of the frequent application to dynamic problems, almost all the existing works about NIPCM for dynamic UP fail to elaborate the implementation process in a straightforward way, which is important to readers who are unfamiliar with the mathematics of the polynomial chaos theory. Meanwhile, very few works have compared NIPCM to IPCM in terms of their merits and applicability. Therefore, the mathematic procedure of dynamic UP via both methods considering parametric and initial condition uncertainties are comparatively discussed and studied in the present paper. Comparison of accuracy and efficiency in statistic moment estimation is made by applying the two methods to several dynamic UP problems. The relative merits of both approaches are discussed and summarized. The detailed description and insights gained with the two methods through this work are expected to be helpful to engineering designers in solving dynamic UP problems.
文摘In this paper the development of reactive software is transformed into a control problem, and the supervisory control theory for discrete event dynamic systems is suggested to solve this control problem. The operating environment under consideration is viewed as a controlled plant, the software under development as the corresponding controller, and the software requirements as the corresponding control objective. This idea leads to a constructive approach of software design, which ensures properties required a priori of the software under development. In this way the validation of the software under development is reduced to the validation of properties independent of implementation process. We reveal the inconsistence in using the concept of reachability to specify software requirements and clarify six different definitions of reachability. Two different definitions of invariance for specifying software requirements are also clarified. We then show how to synthesize the required controller or obtain software design solutions if the underlying software requirements are specified by several new combinations of reachability and invariance. The topic of this paper falls into the scope of software cybernetics that explores the interplay between software and control.
