With the following setup in Dymola, the model in Modelica Standard Library (Modelica.Fluid.Examples.HeatingSystem) would cause a lot of errors about failing to solve nonlinear equations, even though in the end, nonlinear solver handles this issue successfully, but I don't understand this process.
My question is :
Is there some simple example that demonstrates this process with more details?
I think the key problem here is that Dymola prints Error although it can recover from the problem. That is confusing, and will be improved.
Related
Is it possible to extract the ODE System from OpenModelica?
Using the nice GUI of OpenModelica to generate an ODE System which can be solved for further processings for example in Python would be really nice!
I know about the FMI interface, which we use at the moment for our simulations, but due to many bugs and problems which occur especially by the usage of PyFMI, just using ODE system might give us more control and stability in our further research.
I build a model of solar power plant with the Rankine cycle in Dymola, even though the initialization works fine, but at the time of 2840s, there is a failure to solve the nonlinear equations which leads the simulation to stop.
As shown in the following screenshot, Dymola recommends giving better start values, but it doesn't make any sense, because the failure happens during the simulation instead of initialization. And with better start values, the situation doesn't improve at all.
My question is :
How should I deal with the failure to solve nonlinear equations during simulation?
The error message indicates that the solver was not able to find a solution to a nonlinear system of equations in your model. This could mean either that there is no solution to the system or just that the solver is not able to find it.
The first easy steps would be to try a lower tolerance in simulation settings. And to use another solver that might suit better for your problem. Dassl can handle nonlinear systems quite well. If these steps won't work it might be that there just isn't a solution to your problem and you made a wrong assumption or accidentially have a wrong parameter somewhere.
In Dymola, I often meet a nonlinear system initialization failure or maybe a stiff system that is hard to solve in the large thermo-fluid system, but for a simple system, there wouldn't be this kind of problem. My questions are:
So I am wondering how much is the largest capability of solving a nonlinear system model? For example, how many nonlinear equations I could include in my model at most?
Is there any setting in Dymola which allows increasing the capability of solving nonlinear system?
How could I decrease the number of nonlinear equations in the model without damage to the accuracy of the model?
These are pretty difficult questions to be answered in a generally valid fashion. Still I'll try to share some of my experience with Dymola and non-linear systems.
There is no hard number which will limit the size. It depends more on how strongly non-linear the equations are than on their number. I have simulated models with non-linear systems of size 150, which are pretty stable while others of size 10 can brake...
There are multiple perspectives to this
I have worked on some models that made the C-Compiler run out of memory during compilation. If you have this sort of problem, forcing 64Bit compilation by setting Advanced.CompileWith64=2 can help. Then you shouldn't run out of memory any more. This only refers to the size only.
Performance for non-linear systems can be improved by activating DAE-mode by setting Advanced.Define.DAEsolver=true. This does not work with all solvers though.
Additionally to the above it can help to set Advanced.MoveEquationsToDynamics=true, for which the manual states: "It forces the integrator to solve the nonlinear
equations each integrator step and thereby it also updates the initial guesses more often."
As mentioned by Erik, the homotopy()-operator can be very important as it helps the solver converging in case of difficult initialization.
This is very specific to the model. Decoupling can help, e.g. by splitting the system in smaller systems by adding energy storing elements/states. This can be done based on physics of the system and is the preferable solution if possible. As an (more artificial) alternative filter/delays can be added. Usually this has a negative effect on accuracy.
I very much agree with Markus's advice but would also like to remind you about Modelica's homotopy operator. A well-chosen simplified model can greatly help Dymola to initialize a model with a large and difficult non-linear system.
In general good initial guesses are very important when solving non-linear systems. Using homotopy is simply an implicit way to provide these good guesses.
Has anyone tried to implement the Navier Stokes Partial Differential Equations (PDE) in Modelica?
I found the method of the spatial basis functions (SBF) which by means of numerical modifications gets Ordinary Differential Equations (ODE) that could be handled by Dymola.
Regards,
Victor
The aim of the method I was saying before is to convert PDEs in ODEs, so the issues with the CFL coefficient would disappear, the problem is that the Modelica.Fluids elements just define the equations in function of the variables in both ends of each component.
i.e dp=port_a.p-port_b.p
but with that sort of methodology, the variables such as pressure, density, mass flow... would be function also of the surrounding components... it would be a kind of massive interaction between all the components,
I would like to see an example in Modelica, because I hardly haven't found information about that topic linked to Modelica.
Modelica is a language for modeling behavior described by DAEs. As such, as long as you can create a system of ODEs, you should be able to express your problem in Modelica.
However, if your PDEs are hyperbolic, the wave dynamics in the equations might cause some issues with simulation. This is because the CFL condition imposes limits on time steps that an ordinary differential equation solver will be unaware of. If the solver includes error control, it will probably manage to get a solutions but may run quite slow because it won't know how to explicitly limit the simulation step size. If it doesn't include error control and it violates the CFL condition, the system will go unstable. Note, this only applies to systems where the CFL condition applies.
I have been trying to model the Fabry-Perot resonator in simulink. I am not sure if it is right to choose simulink for this task but I have been getting some results, at least. However, I have been also getting an error of algebraic loop when I use a different pair of coupling/reflection parameters. It says,
"Simulink cannot solve the algebraic loop containing
'jblock_multi_MR/Meander2b/Subsystem3/Real-Imag to Complex' at time
6.91999999999991 using the LineSearch-based algorithm due to one of the
following reasons: the model is ill-defined i.e., the system equations do
not have a solution; or the nonlinear equation solver failed to converge
due to numerical issues.
To rule out solver convergence as the cause of this error, either
a) switch to TrustRegion-based algorithm using
set_param('jblock_multi_MR','AlgebraicLoopSolver','TrustRegion')
b) reducing the VariableStepDiscrete solver RelTol parameter so that
the solver takes smaller time steps.
If the error persists in spite of the above changes, then the model is
likely ill-defined and requires modification."
Changing the solver does not help. As a note, I implemented the system in terms of electric fields and complex signals naturally.
thanks for any help.
There is no magic solution for solving algebraic loop issues, as these issues tend to be very model-dependent. Here are a few pointers though:
What are algebraic loops in Simulink and how do I solve them?
How can I resolve algebraic loops in my Simulink model in Simulink 6.5 (R2006b)?
Algebraic Loops in the Simulink documentation
See also this answer to a similar question on SO, with some suggestions for breaking the loop.