Modeling for FCM Simulation User Guide — Nomenclature and Introduction

Version: 3.9.1

1 Nomenclature

Term	Definition
FCM	Fuzzy Cognitive Mapping
FMEA	Failure Mode & Effects Analysis
LOI	Level of Indenture
MADE	Maintenance Aware Design Ecosystem

2 Introduction

This guide is aimed at presenting the modeling approach for Fuzzy Cognitive Mapping (FCM) simulations in MADE, which involves creating and analyzing a functional model of a complex system. Modeling for FCM simulations requires an interdisciplinary complex model that uses material, energy and signal flow categories as interdisciplinary flows to represent.

This guide aims to answer the following question:

"Q: What is FCM Simulation and how should the user create a model for it?"

FCM simulation serves as the basis for:

• Developing a functional model of a complex system
• Designating simulation parameters
• Analyzing system behavior responses: initial (transient) & final (steady-state) responses for each flow property from every injected functional failure mode
• Verification of simulation results by comparison

"A: FCM simulations are suitable for signal and process-based systems that are used to generate simulation response graphs and failure propagation tables. These model outputs are used to qualitatively analyze and troubleshoot system model behavior."

Main advantages of building a model for FCM simulations:

To Model Electrical and 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 unidirectional relationships between any material, signal or energy flow. Examples of systems suitable for FCM modeling are signal treatment or fuel delivery systems.

To Model Specific Engineering Domains. FCM maps the failure path of each flow property, which may be classified even further to accurately represent the functional behavior of a system for a specific domain i.e. electric, mechanic, hydraulic, chemical, and thermal etc.

To Predict Failure Modes and Effects in a complex system. FCM is used to show how any changes in the system design will change the corresponding system failure modes and their effects on the system behavior. FCM and fuzzy set theory are tools for representing and manipulating the type of linguistic knowledge required in a Failure Mode and Effects Analysis (FMEA).

FCM is a method used for the simulation and analysis of complex systems. Creating models for FCM simulation employs the concept of unidirectional material, signal and energy flow across a system.

Figure 1: Modeling characteristics for FCM simulations — diagram showing three inputs (Unidirectional Exchange of Information, Signal/Process Engineering Systems, Engineering Domain Specific) converging into "FCM".

In functional models, causal connections describe the relationship that links an input flow property to an output flow property. These causal connections are labelled with a plus symbol to indicate a directly proportional relationship (increase in input flow causes an increase in output flow and vice versa), while a minus symbol indicates an inversely proportional relationship (increase in input flow causes a decrease in output flow and vice versa).

Functional properties are associated with fuzzy values and linguistic terms e.g. low, moderate, and high, to describe the degree of the relationship (causal strength) between flow properties.

Figure 2 shows an example "Regulate" function on an "Injector Pump" item, with IN FLOWS Liquid (Flow rate — checked), Mechanical-linear (Force / Linear velocity — Linear velocity selected), Mechanical-rotational (Angular velocity / Torque — Torque selected), all wired with "+" causal connections into OUT FLOWS Liquid (Dynamic pressure — checked).

Numerical analysis of FCM is used to trace the increasing and decreasing effects along all failure paths from one property to another (per B. Kosko, Fuzzy cognitive maps, VERAC, San Diego, 1985). Fuzzy inputs (e.g. low, moderate, high) can be processed as well as real-valued inputs (e.g. 1.0, 2.0), which are fed into the causal algebra used to calculate FCM.

FCM simulations follow several rules:

• Transformation of flow properties from input to output may be linear or non-linear
• Several material, signal or energy flow inputs and outputs are allowed for each item
• The behavior of an individual item has no direct impact on the preceding item, unless a feedback connection is established (this routes the output signal back to the preceding item)

For more information, refer to the following guides in MADE Help:

• FCM Simulation & Theory
• Bond & FCM Modeling comparison (see bond-fcm-guide-*.md in this knowledge base)