4 Differences Between FCM & Bond Graph Modeling

4.1 Flow Types Used for FCM/Bond Graph Simulation

The modeling approach for FCM simulation caters for energy, material, and signal flow categories. Within these flow categories, the user can select any number of flow properties in the model (Figure 8: example shows a function "Increase" with IN FLOWS Discrete/Amplitude, Discrete/Amplitude, Electrical/Current, Liquid/Volume all connecting into OUT FLOWS Liquid/Flow rate).

While this modeling approach for FCM enables the user to choose a broader selection of flow and flow properties, all causal connections between flow properties must be created by the user – this can affect modeling time when it comes to large energy-based models. Figure 9 illustrates a function "Provide" with numerous IN FLOWS (Continuous/Data ×2, Liquid/Flow rate+Temperature, Electrical/Current ×2, Liquid/Flow rate+Temperature) each manually cross-connected to two OUT FLOWS (Liquid/Flow rate+Temperature, Liquid/Flow rate+Temperature) — producing a dense web of causal connections that must all be defined by hand.

The modeling approach for Bond Graph simulations is exclusively focused on using the energy flow category. The causal connections created in a model for Bond Graph simulation are related to effort and flow. As a result, these models differ from FCM-compatible models in that they only require one selected flow property per flow. Figure 10 shows a Bond Graph compatible item ("Divide", Bond Type "1-IR (Inertance and Resistance)") with IN FLOWS "Mechanical - rotational" (Angular velocity / Torque, one selected) connecting directly to OUT FLOWS "Mechanical - rotational" (Angular velocity / Torque, one selected).

4.2 Differences between Modeling for FCM & Bond Graph Simulation

MADE models for Bond Graph simulation can represent bi-directional (forwards & backwards direction) exchange of physical energy, whereas models for FCM simulation represent unidirectional (single direction) flow of information that can be material, energy or signal based. Causal connections in models for FCM simulation do not consider flow properties flowing backwards (i.e. back-effects) which are inherently included in bond graph connections.

"Energy flows for FCM simulation represent the energy transferred from one item to another without considering both potential back-effect coming from the second item, and the effects on properties of the transferred energy. Back-effects are inherently included in bond graph links as 'bonds' – these create the bi-directional exchange of energy."

Figure 11 contrasts:

• (Left) Hydraulic flow for FCM simulation transmitted from Linear Control Valve (hydraulic) to Pipe (hydraulic) via Flow Rate → Pressure, labeled "Unidirectional flow (no back-effect)".
• (Right) The same Linear Control Valve → Pipe connection modeled with Bond types 1-R → 0-C, with Flow Rate/Pressure bonds shown bi-directionally, labeled "Bi-directional flow (back-effect is inherently included)".

Figure 12 ("Modeling Power Transmission & Back-Effects for FCM Simulation") shows the Linear Control Valve → Pipe system with explicit dashed feedback arrows labeled "F-" running backward on both the input and output sides of the Flow Rate/Pressure chain, representing the manually-added feedback connections needed to model back-effects in an FCM model.

When modeling for FCM simulations and back-effects need to be considered, the user needs to create a feedback connection to model back-effects. Bond graph modeling is the preferred approach for modeling power transmitting systems where back-effects have a significant impact on power transmission.

4.3 Modeling System Behavior with FCM & Bond Graph Simulations

FCM and Bond simulations propagate functional failures based on polarity effects (negative or positive) of each flow property on the others. The system is operating in a nominal state by default, until a disturbance creates a failure in the system. A functional failure is represented as a deviation from nominal, an increase (high response) or decrease (low response) of a flow property. While both simulations use this same principle, they differ in the way that they calculate the causal dependency of the input flows to the output flows of an item.

The method of setting causal dependency varies with the simulation approach:

• FCM Simulation – Utilizes a causal strength scale (1–10) to determine causal dependency
• Bond Graph Simulation – Utilizes Bond Types to determine the causal dependency

FCM simulation propagates the failure of flow properties based on causal strength between the input and output flow properties for an item. Causal strength is defined using a crisp scale (numerical value from 1 to 10 with increments of 0.1) and is edited by selecting the causal connection between input and output flow properties, then viewing the General tab in the Properties viewer.

Figure 13 shows the Causal Strength scale in the Properties viewer for a "Torque -> Torque" connection on a "Couple" function: Source = Couple Mechanical - rotational Torque (Coupling), Target = Couple Mechanical - rotational Torque (Coupling), Function = Couple, Polarity = Positive (selected) / Negative, Response Filter = No Filter, Acausal checkbox, Causal Strength slider set to 4.99 (scale 1–10).

Once the causal strength between input and output flows for all items has been edited, FCM simulations can now be generated e.g. FTA, Failure Propagation (Propagate All), Failure Injections etc.

Bond graphs propagate failures of flow properties relating to power transmission through a system. In models designed for Bond graph simulation, all causal dependencies and their effects are modeled in terms of effort and flow, regardless of the engineering domain. Effects that significantly influence system power flow are classified under 3 basic Bond types: resistance, compliance, and inertia.

The Bond Graph simulation uses these Bond types and their corresponding passive variables to determine the appropriate system response.

Figure 14 shows a Bond graph compatible model (Driveline system, Mission Profile "Regular Trip") with the "Differential" item selected in the Properties viewer: Function = Divide, Bond Type = "1-IR Rotational Inertia Mass and Resistance", Passive Variables — Inductor: Value 0.9, Initial Value 0.0, Upper/Lower unchecked; Resistor: Value 0.25.