Augmented network model for engineering system design
Olivier de Weck
Last modified: May 30, 2006
AUGMENTED NETWORK MODEL FOR ENGINEERING SYSTEM DESIGN
I. Introduction – Motivation
Models are usually domain specific and have traditionally been even system-specific. Various modeling tools have sprung up to try to accommodate many systems simultaneously, such as state space and nonlinear dynamics models. As system complexity and data quantity creep up, attempts at a unified systems theory have become more rampant. Network theory is one of the fields that has been recently engaged in this effort, even termed « network science ». Network theory tools exist in many domains, and have been used widely without consolidating efforts for at least 40-50 years. In this paper, we would like to examine the relevance of network tools representation and analysis for engineering systems, their benefits and deficiencies, and at the end lay out recommendations for improvement or alternatives.
The overall difficulty with applying simple network models to engineering systems is that often nodes and links or node relationships are not uniform and not transitive. In an acquaintance network, for example, the relation of knowing someone is reversible, thus the network is undirected. All nodes are uniform (even in modeling hierarchies, nodes are of the same type), and all links are the same. For representation purposes geometry or order is irrelevant. This is not the case for most engineering systems, where at any level of abstraction components are assembled or arranged in particular ways to work properly. Moreover, the nodes and links rarely can be put in the same category. These are hybrid networks: in other words, networks comprised of nodes (and maybe links) of different types.
For example, modeling the components of a vehicle, the parts (or subsystems) of an airplane, the states of a formation of flying vehicles, is not as simple as pointing out the nodes and noting down the physical connections. Depending on the level of abstraction chosen, links can mean physical connections, like an electric connector, welded point, influence connections, like magnetic fields, chemical bonds or concentration levels, in fuel mixtures; abstract connections, such as a transportation route. Links and nodes can have different capacities and costs, maintenance routines, dynamics. Link existence can vary with time. All of these properties of real systems make simple graph representations inadequate for a useful model.
This does not mean that simple metrics from a pure graph model could not be useful for engineering analysis. The key in this type of modeling is i) picking the right level of abstraction, ii) encoding the right level of detail. We call this approach “augmented network modeling for engineering design”.
Various fields have applied network modeling to engineering applications, such as operations research (supply chains), electrical engineering (circuit (controls) theory), and more recently systems engineering (new systems of systems approaches). Most have found good algorithms to solve particular problems but met overall difficulty in applying general models due to domain knowledge specificity. Some of the successful models are discrete-continuous state-space models and object-process networks for formation flight vehicle networks and space mission planning .
In this paper, we propose a state-space-like augmented network model, with high-level simple abstract network description and deeper level of engineering detail description content.
We first give examples of real systems models, with their detailed description, which capture the dynamics and provide inherent model for optimization, design and understanding behavior. Then, we describe in detail one of the models and discuss the benefits and deficiencies of network representation and how it can be adjusted.
II. Models – Examples
An augmented network model is an attempt to capture domain-specific knowledge and yet be able to extract and analyze higher-level network properties. This method does not claim to solve the modeling problems of all systems imaginable, and it does require hard additional work for application adaptation. However such a hybrid representation allows a general plug-in of many models to the same network analysis toolbox.
1. Journal publication network for the MIT ESD community
This is a social network example, consisting of 196 journals as nodes: two journals are connected if one faculty member publishes in both. All nodes and links are of the same type and all links are bidirectional by definition. The data is gathered by taking a poll and recording citations.
2. MAPK reference pathway network
This is a biological network example involving proteins participating in the MAPK pathway. Proteins are modeled as nodes and two proteins are connected if they interact. The data is experimentally verified, available from the KEGG database . Nodes are of the same type, links can vary depending on the type of interaction, such as activation or inhibition.
3. Car Frame Assembly Network
Consider the example of a network of passenger car frame components. Individual components are nodes in the component network. The arcs represent physical connectivity between the components. The nodes are not identical: each one of them represents a uniquely different item, even though some nodes might be very similar, i.e. mirror images of each other due to symmetry of the vehicle. This is an example of a mechanical network in which geometry and relative position matters as much as pure connectivity for the proper operation of the system. Each component can be identified by its different name, position with respect to other components and different structure and function.
4. Space transportation network model
There are states in space which a spacecraft can exist in with minimal energy expense (ex. orbiting). State transitions require energy leaps, in the form of fuel burns, provided by the vehicle itself or an external force (another vehicle, by-passing planet etc). Naturally, states can be modeled as nodes and transitions as links, so that the mission time / value is concentrated in the nodes, while the mission cost / energy spent is contained mainly in the links. This is not a perfect assumption, because transitions are not instantaneous and states are not cost-free (ex: stationkeeping and correction maneuvers). Here, neither all nodes, nor all links are of the same type. As it will be explained in the paper, this can be modeled as a tri-partite network, with differentiated time-dependent links.
III. Comparative Analysis, Network Statistics
For all the systems discussed above, general network characteristics such as degree and betweenness distributions, clustering, modularity, pathlengths are analyzed and compared.
These are apparently systems of different domains, size and level of heterogeneity. We discuss the relevance of network modeling in each case, the biases and data collection problems, as well as the implications for analysis and design. For example, social network studies have long been employed to study community structure, functional clusters and prominent nodes. Network structure and topology studies are fairly straightforward to do with homogeneous networks. In biological and technological systems domain knowledge becomes essential. We present limits to connectivity in engineered systems , directionality constraints, link types, levels of abstraction.
In the final analysis chapter of this paper, we show an example of building an augmented network model for the space transportation network  and suggest methodology for a uniform engineering systems nomenclature.
1. Bounova G., de Weck O.L., Graph-theoretical Considerations in Design of Large Telescope Arrays for Robustness and Scalability, AIAA-2005-2063, 1st AIAA Multidisciplinary Design Optimization Specialist Conference, Austin, Texas, April 18-21, 2005
2. Simmons, W.L., Koo, B.H.Y., Crawley, E. Mission Mode Architecture Generation for Moon-Mars Exploration Using an Executable Meta-Language, AIAA-2005-6726, Space 2005, Long Beach, California, August 30 - September 1, 2005
3. Hybrid Control Systems Laboratory, Stanford
4. KEGG database, source: http://www.genome.jp/kegg/pathway.html
5. Dan Whitney, Connectivity Limits of Mechanical Assemblies Modeled as Networks, ESD Working Paper Series
6. Bounova, G., Ahn, J., Hofstetter, W., Wooster, P., Hassan, R., de Weck, O. L., Selection and Technology Evaluation of Moon/Mars Transportation Architectures AIAA-2005-6790, Space 2005, 30 Sept - 1 Aug, Long Beach, California