scholarly journals Least-squares collocation for linear higher-index differential–algebraic equations

2017 ◽  
Vol 317 ◽  
pp. 403-431 ◽  
Author(s):  
Michael Hanke ◽  
Roswitha März ◽  
Caren Tischendorf ◽  
Ewa Weinmüller ◽  
Stefan Wurm
Keyword(s):  
Least Squares ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Least Squares Collocation

scholarly journals Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations—Part 2: the discrete least-squares problem

2021 ◽  
Author(s):  
Michael Hanke ◽  
Roswitha März
Keyword(s):  
Least Squares ◽  
Differential Algebraic Equations ◽  
Collocation Methods ◽  
Discrete Problem ◽  
Algebraic Equations ◽  
Least Squares Collocation ◽  
Least Squares Problem ◽  
Ill Posed ◽  
Natural Settings ◽  
Selection Of

AbstractIn the two parts of the present note we discuss questions concerning the implementation of overdetermined least-squares collocation methods for higher index differential-algebraic equations (DAEs). Since higher index DAEs lead to ill-posed problems in natural settings, the discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. We provide in Part 1 a robust selection of basis functions and collocation points to design the discrete problem whereas we analyze the discrete least-squares problem and substantiate a procedure for its numerical solution in Part 2.

scholarly journals Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations—Part 1: basics and ansatz function choices

2021 ◽  
Author(s):  
Michael Hanke ◽  
Roswitha März
Keyword(s):  
Least Squares ◽  
Differential Algebraic Equations ◽  
Collocation Methods ◽  
Discrete Problem ◽  
Algebraic Equations ◽  
Least Squares Collocation ◽  
Ill Posed ◽  
Present Part ◽  
Natural Settings ◽  
Selection Of

AbstractIn the two parts of the present note we discuss several questions concerning the implementation of overdetermined least-squares collocation methods for higher index differential-algebraic equations (DAEs). Since higher index DAEs lead to ill-posed problems in natural settings, the discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. In the present Part 1, we provide a robust selection of basis functions and collocation points to design the discrete problem. We substantiate a procedure for its numerical solution later in Part 2. Additionally, in Part 1, a number of new error estimates are proven that support some of the design decisions.

Observer Based Fault Detection and Identification in Differential Algebraic Equations

2013 ◽  
Author(s):  
Jason R. Scott ◽  
Stephen L. Campbell
Keyword(s):  
Fault Detection ◽  
Least Squares ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Frequency Filtering ◽  
Detection And Identification ◽  
Fault Detection And Identification ◽  
Filtering Technique

Fault detection and identification (FDI) are important tasks in most modern industrial and mechanical systems and processes. Many of these systems are most naturally modeled by differential algebraic equations. One approach to FDI is based on the use of observers and filters to detect and identify faults. The method presented here uses the least squares completion to compute an ODE that contains the solution of the DAE and applies the observer directly to this ODE. Robustness with respect to disturbances is also addressed by a frequency filtering technique.

Least Squares Based Transient Nonlinear Gas Path Analysis

2005 ◽  
Author(s):  
Tomas Gro¨nstedt
Keyword(s):  
Path Analysis ◽  
Least Squares ◽  
Optimal Estimation ◽  
Equation System ◽  
Differential Algebraic Equations ◽  
System Of Nonlinear Equations ◽  
Algebraic Equations ◽  
Transient Model ◽  
Nonlinear Transient ◽  
Least Squares Estimates

A method for computing least squares estimates for transient nonlinear gas path analysis is derived. The solution to the optimal estimation problem is found by solving a system of nonlinear equations. A single iteration of the equation system requires integrating an extended set of nonlinear ordinary differential algebraic equations (ODAE). The additional differential equations originate from the differentiation of the least squares expression used to define optimality. The numerical efficiency of the extended ODAE algorithm is assessed by comparing it to an optimization based method. To illustrate the derived estimation technique a complete model of the Frank Whittle W1 engine is given within the paper. An example of the implementation of the extended ODAE method is demonstrated in the framework of this model. The performance of the method is also discussed and evaluated on a full nonlinear transient model of the RM12 fighter engine.

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