Model Order Reduction Algorithm

Model validation and design study results are generated from a model that has the maximum possible complexity (baseline model). To improve the simulation efficiency by eliminating elements that do not contribute to outputs of interest, while retaining design variables with physical meaning, an energy-based Model Order Reduction Algorithm is applied to the baseline model. The application of this algorithm requires a model and set of parameters, which we already have, and a rich input to excite all the dynamics of the system for a given scenario.

The activity of each energy element establishes a hierarchy for all the elements. Those elements below a user-defined threshold of acceptable level of activity are eliminated from the model, a reduced model is generated and a new set of governing differential equations is derived.

• Build a model of the system, which is usually (initially, at least) complicated.

• For a given input and system parameters, calculate for each element: Power > Activity > Activity Index

• Sort the activity indices.

• Keep the elements that account for a given activity level, i.e. set a threshold to an arbitrary value (such as 90% for example).

Therefore, to derive a reduced model, an activity threshold must be specified. The threshold is the percentage of the total activity that the reduced model should minimally represent. Given the activity threshold and the relative rank of each element of k elements, the reduced model can be obtained by augmenting (removing) elements from highest to lowest (lowest to highest) rank until the cumulative index exceeds the prescribed activity threshold. The cumulative index, CI, is the sum of the activity indices of the elements incorporated into the model:

Equation 3:

A top-down (highest to lowest) or bottom-up (lowest to highest) method for obtaining a reduced model based on relative activity rank of elements is presented in the figure below, and is similar to an algorithm presented by Louca et al.

Figure 5: Algorithm for obtaining a reduced model via activity indexes [J.A. Kypuros, R.G. Longoria]

Practically, in Simcenter Amesim, the first step is to calculate the activity index of all elements in each submodel of the system. Next, activity indexes are sorted to identify the elements with high and low activity (most and least active). With the activity indexes sorted, we can specify a threshold of the total activity that we want to include in the model. This threshold defines a target limit between retained and eliminated elements of the system.

Note

The procedure of simplification consists in removing the "least active" elements which are the elements having the lowest activity index. Sometimes submodels can be replaced by simpler versions, or they can be totally removed, this leads to the simplification of the whole model.

Note

Please note that the simplifications made by this method apply to the system under a particular duty cycle. The simplification is not necessarily valid for another duty cycle.