Activity Index and I, C, R, S and RS elements

In the bond graph formalism, energy is conserved, power flow paths can be identified, and power flow associated with elements and their connections can be readily determined.

Generalized inertias I and capacitances C store energy as a function of the system state variables, which are generalized momenta and displacements. The time derivatives of generalized momentum p and displacement q are generalized effort e and flow f, the product of which is power.

Generalized resistors R remove energy from the system, and have a constitutive law relating generalized effort to generalized flow. Sources of effort and flow (Se and Sf) represent ports through which the system interacts with its environment.

I, C and R elements are the most common in Simcenter Amesim™ software. However, S sources have been implemented in components where energy is supplied in an implicit manner (i.e. without flowing explicitly through any of its physical ports). We can also have resistive RS sources to describe situations where energy is both:

• converted from another energy form into heat,

• used in the system by another component (e.g. transmitted to another component of the circuit through a thermal port) or by the component itself (e.g. kept in the component to increase its temperature), or both.

Resistive sources are mainly used in libraries that mix a bond graph formalism with thermal effects.

The Activity Index facility is a powerful analysis tool based on energy transfer in the submodels of a system. The energy is split up into physical types physical types:

• R: physical types dissipation dissipation

• C: physical types capacitance capacitance

• I: physical types inertia inertia

• S: physical types source source

• RS: physical types resistive source resistive source

and into the following physical domains:

• Hydraulic

• Mechanical

• Electrical

• Thermal

• Magnetic

• Thermodynamic

Taking the mechanical domain as an example, it mainly has components of I, C and R physical types. These can be found in the following submodels:

	MAS001: mechanical inertia
	SPR000A: mechanical capacitance
	DAM000: mechanical dissipation
	For a given domain, one submodel can have more than one physical type: SD0000A: mechanical capacitance and mechanical dissipation

Other examples of I, C, R elements are presented below.

Figure 4: Examples of some I, C, R elements in Simcenter Amesim

The Activity Index can identify the most energy-active components of a system and the most energy-passive components. It can also be used to simplify complex models. This is done by eliminating, where possible, the most energy-passive components. The study of the activity indexes in each submodel of a system can sometimes allow you to reduce the model complexity down to a level which nonetheless remains accurate enough to simulate the phenomena being studied.