Hierarchical Structural Analysis Method for Complex Equation-Oriented Models

Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening of the hierarchical models into an equation system for analysis. However, the large-scale equations in complex models make structural analy...

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Autores principales:	Chao Wang, Li Wan, Tifan Xiong, Yuanlong Xie, Shuting Wang, Jianwan Ding, Liping Chen
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	equation-oriented models model check structural analysis nonlinear-algebraic equation model differential-algebraic equation model Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/58e358c8d31a43ff8738fe237c7adb80
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id	oai:doaj.org-article:58e358c8d31a43ff8738fe237c7adb80
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spelling	oai:doaj.org-article:58e358c8d31a43ff8738fe237c7adb802021-11-11T18:14:05ZHierarchical Structural Analysis Method for Complex Equation-Oriented Models10.3390/math92126602227-7390https://doaj.org/article/58e358c8d31a43ff8738fe237c7adb802021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2660https://doaj.org/toc/2227-7390Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening of the hierarchical models into an equation system for analysis. However, the large-scale equations in complex models make structural analysis difficult. Aimed to address the issue, this study proposes a hierarchical structural analysis method by exploring the relationship between the singularities of the hierarchical equation-oriented model and its components. This method obtains the singularity of a hierarchical equation-oriented model by analyzing a dummy model constructed with the parts from the decomposing results of its components. Based on this, the structural singularity of a complex model can be obtained by layer-by-layer analysis according to their natural hierarchy. The hierarchical structural analysis method can reduce the equation scale in each analysis and achieve efficient structural analysis of very complex models. This method can be adaptively applied to nonlinear-algebraic and differential-algebraic equation models. The main algorithms, application cases and comparison with the existing methods are present in this paper. The complexity analysis results show the enhanced efficiency of the proposed method in the structural analysis of complex equation-oriented models. Compared with the existing methods, the time complexity of the proposed method is improved significantly.Chao WangLi WanTifan XiongYuanlong XieShuting WangJianwan DingLiping ChenMDPI AGarticleequation-oriented modelsmodel checkstructural analysisnonlinear-algebraic equation modeldifferential-algebraic equation modelMathematicsQA1-939ENMathematics, Vol 9, Iss 2660, p 2660 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	equation-oriented models model check structural analysis nonlinear-algebraic equation model differential-algebraic equation model Mathematics QA1-939
spellingShingle	equation-oriented models model check structural analysis nonlinear-algebraic equation model differential-algebraic equation model Mathematics QA1-939 Chao Wang Li Wan Tifan Xiong Yuanlong Xie Shuting Wang Jianwan Ding Liping Chen Hierarchical Structural Analysis Method for Complex Equation-Oriented Models
description	Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening of the hierarchical models into an equation system for analysis. However, the large-scale equations in complex models make structural analysis difficult. Aimed to address the issue, this study proposes a hierarchical structural analysis method by exploring the relationship between the singularities of the hierarchical equation-oriented model and its components. This method obtains the singularity of a hierarchical equation-oriented model by analyzing a dummy model constructed with the parts from the decomposing results of its components. Based on this, the structural singularity of a complex model can be obtained by layer-by-layer analysis according to their natural hierarchy. The hierarchical structural analysis method can reduce the equation scale in each analysis and achieve efficient structural analysis of very complex models. This method can be adaptively applied to nonlinear-algebraic and differential-algebraic equation models. The main algorithms, application cases and comparison with the existing methods are present in this paper. The complexity analysis results show the enhanced efficiency of the proposed method in the structural analysis of complex equation-oriented models. Compared with the existing methods, the time complexity of the proposed method is improved significantly.
format	article
author	Chao Wang Li Wan Tifan Xiong Yuanlong Xie Shuting Wang Jianwan Ding Liping Chen
author_facet	Chao Wang Li Wan Tifan Xiong Yuanlong Xie Shuting Wang Jianwan Ding Liping Chen
author_sort	Chao Wang
title	Hierarchical Structural Analysis Method for Complex Equation-Oriented Models
title_short	Hierarchical Structural Analysis Method for Complex Equation-Oriented Models
title_full	Hierarchical Structural Analysis Method for Complex Equation-Oriented Models
title_fullStr	Hierarchical Structural Analysis Method for Complex Equation-Oriented Models
title_full_unstemmed	Hierarchical Structural Analysis Method for Complex Equation-Oriented Models
title_sort	hierarchical structural analysis method for complex equation-oriented models
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/58e358c8d31a43ff8738fe237c7adb80
work_keys_str_mv	AT chaowang hierarchicalstructuralanalysismethodforcomplexequationorientedmodels AT liwan hierarchicalstructuralanalysismethodforcomplexequationorientedmodels AT tifanxiong hierarchicalstructuralanalysismethodforcomplexequationorientedmodels AT yuanlongxie hierarchicalstructuralanalysismethodforcomplexequationorientedmodels AT shutingwang hierarchicalstructuralanalysismethodforcomplexequationorientedmodels AT jianwanding hierarchicalstructuralanalysismethodforcomplexequationorientedmodels AT lipingchen hierarchicalstructuralanalysismethodforcomplexequationorientedmodels
_version_	1718431886723776512

Hierarchical Structural Analysis Method for Complex Equation-Oriented Models

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