5 When to Use FCM/Bond Graph Modeling Techniques

Deciding whether a system should be modeled with Bond or FCM simulation ultimately depends on whether back-effects have a significant impact on the system flows. If back-effects are significant, then feedback flows need to be modeled. Since modeling for Bond Simulation automatically defines feedback flows, this is a more efficient modeling approach. If feedback is not important, or the model focuses on material or signal flows, then modeling for FCM simulation is a more appropriate modeling approach.

5.1 Applications for FCM Simulation Compatible Models

5.1.1 Modeling Electrical & Process Engineering Systems

FCM is the preferred approach to model systems whose main purpose is to provide any material or signal outputs as it maps relationships between any material, signal, or energy flow. Examples of systems suitable for FCM modeling are signal treatment or fuel delivery systems.

Figure 15 shows a modeled LAN system using both energy and signal flow categories: IN → {UPS (Current), Firewall (Data)} → Gateway Router → {Switch 1, DMZ} → {Subnet A, Subnet B, Subnet C} → OUT, with Current and Data flow lines throughout.

5.1.2 Modeling Specific Engineering Domains

FCM uses energy, signal, or material flows. Material flows feature not only effort/flow properties (pressure, flow rate) but also other secondary properties (e.g. contamination, viscosity) and as such, are suited for specific engineering domain applications.

Figure 16 shows a modeled Rocket Engine with energy, material & signal flow categories: IN → {Fuel Pump (Flow rate/Current/Mass flow rate), Engine Control Unit (Data/Data/Data/Voltage), Oxidizer Pump (Static pressure/Mass flow rate)} → Control Valve 1/2/3 → Pre-combustor → Turbine (Angular velocity/Mass flow rate) → Combustion Chamber (Pressure) → Exhaust Nozzle (Mass flow rate/Data) → OUT.

5.1.3 Predict Failure Modes & Effects in a Complex System

After a model has been developed, FCM simulation is used to show how any changes in system configuration will affect corresponding system failure modes and their effects on the system behavior.

FCM simulation and fuzzy set theory are powerful and effective tools for representing and manipulating the type of linguistic knowledge required in a Failure Mode and Effects Analysis (FMEA).

Figure 17 shows a MADE FMECA Report (FMECA (RPN, PHMT)) generated from a model developed for FCM simulation, with a bookmark tree (Engine, Governor, Injector Pump, Lift Pump) and a tabular report with columns: Item No., Item/Physical Description, Function/Functional Narrative, Failure Mode, Cause of Failure (Mechanism, Cause, Next Higher Level, End Effects), Detection Methods, Compensating Provisions, and Criticality (O, S, D, RPN) — shown alongside the underlying Diesel Engine system model diagram.

FCM Modeling Workflow (Figure 18)

Figure 18 depicts "WF04: Create FBD Model for FCM Simulations", structurally similar to the Bond Modeling workflow (WF03, see the Bond Modeling Guide) but for FCM.

Pre-requisites:

• A. MADE Project: a configured project.
• B. Bill of Materials (BOM): establishes the system configuration to build the functional block diagram (FBD) model.

Flowchart steps:

1. Create Model Item
2. Define Function(s)
3. Define Functional Flows
4. All Model Items Created? → No: loop back to step 1 / Yes: continue
5. Connect Functional Flows
6. Define Model Item Details (fed by: General Properties, Advanced Properties, Product Characteristics)
7. Define Flow Property General Details (fed by: Display Name, Unit, Initial Value, Internal Damping)
8. Define Functional Flow Causality Details (fed by: Polarity, Response Filter, Acausality, Causal Strength)
9. All Model Items Defined? → No: loop back to step 6 / Yes: continue
10. Review FCM Response Simulations
11. Responses Acceptable? → No: loop back to step 6 / Yes: continue
12. FBD Model For FCM Created → Propagation Table

Detailed Descriptions:

1. Create model items with 'New Item' options under 'Modeling' in the main menu bar or via the context menu opened on the system model viewer canvas.
2. Define function(s) in the Functions Editor, accessed by 'Functions' via the right-click context menu opened on the model item. Click and drag the relevant function from the Function taxonomy and place on the canvas.
3. Click and drag the relevant functional flows from the Functional Flow taxonomy list onto the relevant in- or out-put. Connect Flow Properties clicking and dragging from In Flows to Out Flows.
4. Continue creating model items, defined with functions and functional flows.
5. Connect functional flows between model items by clicking and dragging from the output of one item, to the input of the other. Only same functional flows will connect.
6. Select a model item and define General details in the Properties viewer, which overlaps with Advanced details accessed by 'Advanced Properties' via the context menu opened on the model item. Also define Product Characteristics, if necessary.
7. Access Functions Editor and select a functional flow property to define General details in the Properties viewer.
8. Select a functional flow connection between flow properties to define causality details in the Properties viewer.
9. Select another model item, repeating previous steps until all are defined with the necessary details for FCM simulation.
10. Execute 'Propagate All' in the context menu opened on the system model viewer canvas, 'Select all' to view all functional flows and then 'Propagate', to review FCM response simulations.
11. Following review of FCM response simulations in the Propagation Table viewer, deem responses unacceptable, alter functional flows until acceptable, including creating model items.
12. FBD Model created for FCM simulations.

Outputs:

• Propagation Table: tabulated results of failure propagations throughout system model for FCM response simulations, exportable as a .csv file.

5.2 Applications for Bond Graph Simulation Compatible Models

5.2.1 Modeling Multi-Disciplinary Engineering Systems

Modeling for Bond Graph simulation is an intuitive approach that uses a physical, dynamic system comprised of items that interact by exchanging energy. This means bond graph modeling can model systems that cross engineering domains (electrical, mechanical, hydraulic, acoustical, thermodynamic, etc.)[^1]. The focus on energy exchange between items and the transformation of energy from one form into another implies that bond graphs are particularly suited for modeling multidisciplinary engineering systems.

Figure 19 shows multiple engineering domains modeled in a Bond Graph compatible model: IN → Control Valve (1-R, Pressure/Flow rate) → Hydraulic Cylinder (Piston) (0-C, Pressure) → Power Transformer (Hydraulic cylinder) (TF, Force) → Inertia Load (1-IR, Linear velocity) → OUT.

5.2.2 Modeling Time Continuous Systems

The nodal structure of bond graph models complies with conservation laws in physics. These models provide a set of equations and the ability to model continuous and non-linear systems that combine multiple domains.

Since physical processes are continuous with respect to time and space, bond graphs are especially suited for modeling time continuous systems.

Figure 20 shows a Bond Graph & Bond Equation Set of a Hydraulic System model. Bond Graph: 1 (Control Valve, R@4) — 0 (Hydraulic Cylinder/Piston, C@2) — TF (PowerTransformer/Hydraulic..) — 1 (Inertia Load, I@1, R), with the "Bond Model is Controllable" notification, and the following full equation set:

1.  1.Inductance = 1.Inductance
2.  1.Flow = 1.Inductor State / 1.Inductance + Inductor initial condition
3.  2.Capacitance = 2.Capacitance
4.  2.Effort = 2.Capacitor State / 2.Capacitance + Capacitor initial condition
5.  3.Resistance = 3.Resistance
6.  4.Resistance = 4.Resistance
7.  8.Ratio = 8.Ratio
8.  3.Flow = 1.Flow
9.  5.Effort = 2.Effort
10. 6.Effort = 2.Effort
11. 7.Flow = 1.Flow
12. 3.Effort = 3.Flow * 3.Resistance
13. 4.Effort = 5.Effort
14. 6.Flow = 7.Flow / 8.Ratio
15. 7.Effort = 6.Effort / 8.Ratio
16. 1.Effort = 7.Effort - 3.Effort
17. 4.Flow = 4.Effort / 4.Resistance
18. 1.Inductor State = Integral(1.Effort)
19. 5.Flow = 4.Flow

This is a directly reusable worked example of how MADE derives a full symbolic equation set (inductor/capacitor state integrals, resistor Ohm's-law-style relations, transformer ratio relations, and junction effort/flow balance equations) from a Bond Graph model — useful as a template for verifying or hand-deriving Bond Graph equations for other systems.

5.2.3 Verify the Completeness of a Model

Bond graph modeling verifies that all causalities are correctly assigned and that the physical system is completely represented. The user of bond graphs can easily determine what the dynamic effects of various elements are as it only deals with power variables (e.g. effort and flow, pressure and flow rate, voltage and current, force and velocity).

Figure 21 shows the Bond Graph editor in MADE detecting an uncontrollable model ("Bond Model is not Controllable") for a complex Hydraulic System with many interconnected TF, 0-, 1-junctions, C, I, R, and GY elements (Main Rotor, Accessory Gearbox 1/2, Shaft 1/2, Rotor 1/2, Hydraulic Pump 1/2, Hydraulic Line 1/2, Filter 1/2, Spring-TV 1/2, Transfer Module 1/2, Tail Piston, Tail Actuator, Primary Piston, Primary Actuator, Flow Control Valve 4/5/6, Junction 2, Cyl.) — demonstrating a large multi-branch rotorcraft-style hydraulic/drivetrain Bond Graph.

Bond Modeling Workflow (Figure 22)

Figure 22 reproduces the same "WF03: Create FBD Model for Bond Simulations" workflow diagram documented in detail in the Bond Modeling Guide (see bond-modeling-guide-workflow.md).

5.3 Conclusion

This guide outlined two modeling approaches for a functional model of a complex system for the purposes of FCM and Bond Graph simulation. This guide covers the goals of each modeling approach and how it can be used to simulate a complex system. The usage of one modeling approach or the other should be consistent with the purpose of the model in terms of the analyses or behavioral simulation of interest.

While modeling for FCM simulation allows a freer selection of unidirectional flow categories (signal, material, or energy), all causal relations must be created manually which can affect modeling efficiency in large models. Models compatible with FCM simulation are used for signal and process-based systems while models compatible with the Bond Graph simulation method are the preferred approach for modeling power transmission systems, especially when different physical domains are involved.

FCM and Bond Graph simulations are used to generate simulation response graphs and failure propagation tables to investigate the propagation of failures in a system.

The modeling approaches in MADE give the user control over the type of modeling required for a given simulation approach. This requires understanding physical and mathematical relationships, knowledge of hardware and familiarity with the modeling process. The graphical interface, flexibility in model representation, ability to store developed models for future use, and real-time operation of hardware-in-the-loop (HWIL) simulation makes MADE modeling an efficient method of generating system simulations and identifying critical items with the relevant failure analyses.

[^1]: Jan F. Broenink, Introduction to Physical Systems Modelling with Bond Graphs, University of Twente, Netherland, 1999.