Fast and accurate simulation of fluid power circuits in the presence of small volumes using advanced methods and models for numerical stiffness elimination
Ustinov, Stanislav (2023-06-02)
Väitöskirja
Ustinov, Stanislav
02.06.2023
Lappeenranta-Lahti University of Technology LUT
Acta Universitatis Lappeenrantaensis
School of Energy Systems
School of Energy Systems, Konetekniikka
Kaikki oikeudet pidätetään.
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In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of Lappeenranta-Lahti University of Technology LUT's products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_ standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink.
Julkaisun pysyvä osoite on
https://urn.fi/URN:ISBN:978-952-335-942-0
https://urn.fi/URN:ISBN:978-952-335-942-0
Tiivistelmä
The modeling and simulation of fluid power systems are essential parts of the real-time simulation of virtual prototypes of mobile working machines. In several cases, in the dynamic simulation of such fluid power systems, a longer simulation time is required. This makes the traditional mathematical models inefficient for real-time simulations, particularly when simulating fluid power systems because of the small volumes in stiff differential equations of pressure. On the other hand, the accuracy and stability of the traditional models also suffer from a numerical stiffness problem, while these models are accelerated by a reduction of the integration time steps.
To solve the problem of small volumes in stiff fluid power circuits, different explicit and implicit solvers are used. The most common methods are pseudo-dynamic methods and singular perturbation theory-based solvers. This dissertation, in addition to the existing methods, demonstrates various advanced methods and models to improve the simulation speed of stiff fluid power circuits in the presence of small volumes, and to keep the accuracy at a high level compared to the slower traditional mathematical models of such circuits.
Based on the results of the experiments performed with several fluid power circuits, which contained small volumes in their structure, the model for the Advanced Pseudo-Dynamic Solver was formulated. There are two main differences between the Advanced Pseudo- Dynamic Solver in comparison with the classical pseudo-dynamic solver. First, the calculation of the outlet volume flow rate related to the small volume is included in the inner loop of the solver, which allowed the numerical stability of the solution to be increased. In addition, the adaptive convergence criterion is proposed in the model, which allowed to increase the simulation speed and accuracy of pressure and piston position response. Obtained simulation results confirmed that the proposed solver is much more efficient in the solution of the fluid power circuits than the conventional lumped fluid theory-based method, as well as the classical pseudo-dynamic solver. Finally, the Advanced Pseudo- Dynamic Solver-based model can be calculated faster than the conventional model of the fluid power circuit with small volumes owing to the possibility of the application of a larger integration time step.
Another effective method for the simulation of fluid power circuits is the Method of Multiple Scales. This method is based on the singular perturbation method used earlier for the real-time simulation of stiff fluid power circuits in the presence of small volumes. The results of the research showed that the method of multiple scales is much more accurate than the traditional mathematical model of fluid power circuits. Even more, the method demonstrated better accuracy performance compared to the classical singular perturbation theory-based method due to the elimination of cumulative error. The tested simulation speed of the proposed method allows for the simulation of stiff fluid power systems in real time and makes it possible to use this method in different real-time or faster than real-time applications.
The third method proposed in this dissertation is a novel hybrid model for the simulation of stiff fluid power circuits. The main feature of the model is the utilization of a recurrent neural network instead of stiff differential equations of pressure with small volume. At the same time, the dynamics of the rest system are traditionally presented with algebraic and differential equations. The testing results of the introduced hybrid model showed that this novel method can reduce the simulation time, which makes the model suitable for real-time applications. Moreover, the accuracy of the model remains at a fairly high level compared to traditional mathematical models.
To solve the problem of small volumes in stiff fluid power circuits, different explicit and implicit solvers are used. The most common methods are pseudo-dynamic methods and singular perturbation theory-based solvers. This dissertation, in addition to the existing methods, demonstrates various advanced methods and models to improve the simulation speed of stiff fluid power circuits in the presence of small volumes, and to keep the accuracy at a high level compared to the slower traditional mathematical models of such circuits.
Based on the results of the experiments performed with several fluid power circuits, which contained small volumes in their structure, the model for the Advanced Pseudo-Dynamic Solver was formulated. There are two main differences between the Advanced Pseudo- Dynamic Solver in comparison with the classical pseudo-dynamic solver. First, the calculation of the outlet volume flow rate related to the small volume is included in the inner loop of the solver, which allowed the numerical stability of the solution to be increased. In addition, the adaptive convergence criterion is proposed in the model, which allowed to increase the simulation speed and accuracy of pressure and piston position response. Obtained simulation results confirmed that the proposed solver is much more efficient in the solution of the fluid power circuits than the conventional lumped fluid theory-based method, as well as the classical pseudo-dynamic solver. Finally, the Advanced Pseudo- Dynamic Solver-based model can be calculated faster than the conventional model of the fluid power circuit with small volumes owing to the possibility of the application of a larger integration time step.
Another effective method for the simulation of fluid power circuits is the Method of Multiple Scales. This method is based on the singular perturbation method used earlier for the real-time simulation of stiff fluid power circuits in the presence of small volumes. The results of the research showed that the method of multiple scales is much more accurate than the traditional mathematical model of fluid power circuits. Even more, the method demonstrated better accuracy performance compared to the classical singular perturbation theory-based method due to the elimination of cumulative error. The tested simulation speed of the proposed method allows for the simulation of stiff fluid power systems in real time and makes it possible to use this method in different real-time or faster than real-time applications.
The third method proposed in this dissertation is a novel hybrid model for the simulation of stiff fluid power circuits. The main feature of the model is the utilization of a recurrent neural network instead of stiff differential equations of pressure with small volume. At the same time, the dynamics of the rest system are traditionally presented with algebraic and differential equations. The testing results of the introduced hybrid model showed that this novel method can reduce the simulation time, which makes the model suitable for real-time applications. Moreover, the accuracy of the model remains at a fairly high level compared to traditional mathematical models.
Kokoelmat
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