Structural analysis for static and dynamic models

Abstract Modeling and simulation is an expanding area in several domains. In this work, the currently available methods for detecting inconsistencies in systems of equations coming from both static and dynamic models are briefly reviewed. For the dynamic case, a new algorithm is proposed. The proposed algorithm allows a detailed diagnosis of the dynamic degrees of freedom and valid initial conditions of differential-algebraic equation (DAE) systems. The algorithm is scalable for large problems and is a promising diagnosis tool to spread the usage of equation-oriented dynamic simulators.

[1]  Benjamin Andrew Allan A more reusable modeling system , 1998 .

[2]  Wolfgang Marquardt,et al.  Getting around consistent initialization of DAE systems , 1997 .

[3]  C Berge,et al.  TWO THEOREMS IN GRAPH THEORY. , 1957, Proceedings of the National Academy of Sciences of the United States of America.

[4]  W. Marquardt,et al.  Structural analysis of differential-algebraic equation systems—theory and applications , 1995 .

[5]  Timothy A. Davis,et al.  Algorithm 837: AMD, an approximate minimum degree ordering algorithm , 2004, TOMS.

[6]  R. Bachmann,et al.  ON METHODS FOR REDUCING THE INDEX OF DIFFERENTIAL ALGEBRAIC EQUATIONS , 1990 .

[7]  J. F. Boston,et al.  SOFTWARE: TACKLING TOUGHER TASKS , 1993 .

[8]  Hans Olsson,et al.  Dynamic Selection of States in Dymola , 2000 .

[9]  Reinhard Diestel,et al.  Graph Theory , 1997 .

[10]  Wolfgang Marquardt,et al.  Trends in computer-aided process modeling , 1996 .

[11]  Iain S. Duff,et al.  Computing the structural index , 1986 .

[12]  Paul I. Barton,et al.  Differential-Algebraic Equations of Index 1 May Have an Arbitrarily High Structural Index , 1999, SIAM J. Sci. Comput..

[13]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[14]  C. Pantelides The consistent intialization of differential-algebraic systems , 1988 .

[15]  Argimiro Resende Secchi,et al.  Direct initialisation and solution of high-index DAE systems , 2005 .

[16]  D. V. Steward On an Approach to Techniques for the Analysis of the Structure of Large Systems of Equations , 1962 .

[17]  J. Pryce A Simple Structural Analysis Method for DAEs , 2001 .

[18]  William Johns,et al.  Computer‐Aided Chemical Engineering , 2011 .

[19]  Sven Erik Mattsson,et al.  Simulation of object-oriented continuous time models , 1995 .

[20]  Ignacio E. Grossmann,et al.  Systematic Methods of Chemical Process Design , 1997 .

[21]  C. C. Pantelides,et al.  A modelling and simulation language for combined lumped and distributed parameter systems , 1996 .

[22]  W. Morton,et al.  An equation analyser for process models , 1998 .

[23]  Kazuo Murota,et al.  Matrices and Matroids for Systems Analysis , 2000 .

[24]  Constantinos C. Pantelides,et al.  SpeedUp—recent advances in process simulation , 1988 .

[25]  Patrick R. Amestoy,et al.  An Approximate Minimum Degree Ordering Algorithm , 1996, SIAM J. Matrix Anal. Appl..

[26]  Iain S. Duff,et al.  On Algorithms for Obtaining a Maximum Transversal , 1981, TOMS.

[27]  C. W. Gear,et al.  Differential-Algebraic Equations , 1984 .

[28]  C. W. Gear,et al.  Differential-algebraic equations index transformations , 1988 .

[29]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[30]  R. W. H. Sargent,et al.  The decomposition of systems of procedures and algebraic equations , 1978 .

[31]  Arthur W. Westerberg,et al.  Thoughts on a future equation-oriented flowsheeting system☆ , 1985 .

[32]  N. S. Mendelsohn,et al.  Coverings of Bipartite Graphs , 1958, Canadian Journal of Mathematics.

[33]  N. Nedialkov,et al.  Solving Differential-Algebraic Equations by Taylor Series (I): Computing Taylor Coefficients , 2005 .

[34]  Peter Fritzson,et al.  Automated Static Analysis of Equation-Based Components , 2004, Simul..

[35]  Argimiro Resende Secchi,et al.  EMSO: A new environment for modelling, simulation and optimisation , 2003 .