Automatic linearization

Automatic linearization

An automatic linearization run is a specific run that produces information on embedded dynamics in a system over a simulation time range. The option is compatible with implicit and explicit models; it is not compatible with fixed time step simulation.

A direct access to launch such a simulation run is provided through a dedicated button. During the simulation, linearizations are performed automatically at regular times and at times where solving difficulties might be detected.

• The regular times are based on an increment defined by the parameter Minimal number of linearization. By default the value is set to 2. This means that one linearization is performed at time 0s and another one at the final time of the simulation.

• The additional times are based on a specific algorithm that detects events for which the solver encounters issues.

As a result, outputs of automatic linearization are from a set of non-uniformly distributed times.

Outputs of the automatic linearization mode

The automatic run makes it possible to gather information on dynamics during the simulation time range. It provides information on eigenvalues at the linearization times on the ongoing simulation time range.

This information includes:

• The properties of the eigenvalues: A table lists all eigenvalues for the selected time linearization with the values of the frequency, the damping ratio, the fixed time step for explicit Euler's method, and the real/imaginay parts. Columns can be sorted by ascending or descending order.

• The top contributing state variables: For each eigenvalues the participation factor of each state variable is computed for this eigenfrequency. The top ones are then displayed and give insight into which components of the system contribute the most.

• The model pertinence on frequencies of interest: This additional data shows you the balance between the level of complexity of the model and the modeling objectives.

• The maximal eigenfrequencies and Euler's method stability: These reports are useful when the goal of model reduction is exporting to Real-Time target. The use of explicit Euler's solver involves a maximal fixed time step for numerical stability.

Parameterization of automatic linearization mode

Triggering the automatic linearization mode can be done in two ways:

• Starting a run from the frequencies tab in the Performance Analyzer.

• Selecting the automatic linearization option in the Run Parameters window.

The accuracy of the computed outputs might depend on the sample that is defined to retrieve information through this specific option. Setting this value is important as validity of computed information depends on the sampling.

There are two ways to specify the minimal sample at which these computations are performed:

• Setting the minimal linearization time in the Performance Analyzer.

• Setting the minimal time interval in the Run Parameters window.

Note

• Performing automatic linearization and thus computing eigenvalue properties has an additional cost compared to the original simulation cost.

• Accuracy of analysis information might depend on the number of computations performed to get this information. The finer the grid for these computations, the more valuable the information produced but also the more expensive the automatic linearization run.

If no Jacobian is produced during the integration (i.e. the Simcenter Amesim solver is only performing Adams steps), then no information will be produced as outputs of the automatic linearization run.

Limitations of computed information

Although automatic linearization allows you to obtain valuable information for fixed step integration of the current explicit system, you need to be aware of the validity domain of such information:

• The displayed value for the Euler fixed step solver has been computed for the ongoing system and a set of parameters: changing any parameter in this configuration might also change stability conditions for the analyzed system and thus lead to new stability constraints.

• The displayed value for the Euler fixed step solver has been computed based on information provided during the specified simulation time range. Sometimes other dynamics appear later in time than the currently-provided final time. In this case these dynamics might violate the stability constraint expressed by the produced information.

• The computation information during the automatic linearization mode is based on linearization assumptions that might be locally violated during the simulation. Moreover using the stability boundary as a direct value for fixed step simulation might not always be a good idea. This could produce spurious oscillations in the computed results. Even if this information is often valuable as it is, adjusting the boundary for the Euler Fixed step with a safety factor (typically of value around 0.8 to 0.9) might help for the real fixed step simulation of the system concerned.