An extended hierarchical graph-based building model for design and engineering problems
Introduction
There are many well-known methods of representing knowledge in computer systems. Selection of the appropriate structure for knowledge representation and manipulation is a key issue in constructing knowledge-based systems. On the one hand, such a structure should be hierarchical as hierarchy generating techniques are commonly used for acquiring, analysing and modelling knowledge, in particular to build taxonomies and other complex structures. On the other hand, when the chosen structure has a graph-based form, graph methods make it possible to integrate hierarchical object representations and the process of generating their graph models.
This paper continues research into advanced hierarchical graph structures used for knowledge representation in complex engineering problems. The proposed approach has been inspired by studies on navigating mobile robots inside buildings [1]. Moreover, a graph-based representation of a building design facilitates the communication between different specialists and consultants which turn the project from design to construction. They should adhere to the design specification as usually the construction should be compatible with the previously created design. Changes required during project realization can be introduced to the related graph hierarchy and then knowledge-based reasoning about existing conflicts with elements of other hierarchies can be performed. The considered multi-hierarchical graph representation of designs allows us also to encode information which is not included in their BIM (Building Information Modelling) descriptions [2], like assignment of spaces to different departments. The used graph structures can be saved in the GraphML format and then imported to IFC (Industry Foundation Classes) models [3]. As the IFC format is an interoperable BIM standard for CAD applications, there is a possibility of adding semantic information to extend the BIM visualisation mode. Therefore, the proposed new hierarchical graph model is a useful contribution to representing, understanding and processing information in the domains of computer-aided architectural design, construction industry and robotics.
Up to now, in the process of designing building layouts, the hierarchical hypergraphs have been used to represent design drawings [4]. As these hypergraphs were hierarchical they enabled us to express hierarchical dependencies between different parts of designs, like inclusion of rooms in larger spaces. Additionally, there was the possibility of specifying relations between components represented by hyperedges having different parent hyperedges and nested on different levels of hierarchy. Moreover, the hypergraph hierarchy reflected the top-down way of the design solution development and gave the possibility to consider the design only on the interesting hierarchy levels.
However, in the research towards designing multi-storey buildings [5] it turned out that such a representation is not sufficient to effectively model their layouts. In such a design there exist many different types of relations between design parts, which cannot be expressed with a single hierarchy. For instance, different hierarchies are generally required for geometrical and functional dependencies. Similarly, communication paths between floors and elevator shafts cannot be expressed by means of the space hierarchy for single floors.
This paper proposes a new model of building layouts in the form of a graph-based representation with many hierarchies. As many multi-argument relations between components can be expressed by hierarchical arrangement of these components in the graph structure, in order to simplify our considerations, the model is restricted to contain only binary relations between components, which means that graph nodes are connected by simple edges instead of hyperedges.
The robotic domain will be used to exemplify the proposed approach. Multi-hierarchical graph structures encoding knowledge about buildings are useful for robot control algorithms as they facilitate the reasoning process by reducing the number of data to be analysed. The interesting levels of hierarchy can be selected, and only the information related to these levels can be considered.
The paper is organized as follows. Section 2 describes the related work. In Section 3 the proposed graph-based multi-hierarchical representation of design objects, which is the main contribution of this paper, is defined. The new notions related to this structure, like a single view and a view are introduced. Section 4 contains the case study, where the benefits of using the proposed building layout representation by a mail delivery robot operating in a multi-storeyed building are discussed. The paper ends with a conclusion.
Section snippets
Related work
Graphs are commonly used to model relations in many systems. They can be used in design systems to model topological relations between components and in databases to model logical relations between objects. Graphs are also used to model data and control flow or specification and analysis of software systems. The research very often concentrates on graphs without hierarchy – graphs, CP-graphs [6], hypergraphs [7]. In many real applications, modelling systems by plain graphs (graphs where edges
The graph-based representation of layouts
In this section the extended graph-based data structures, which better reflect the intrinsic nature of design objects, are described. They express geometrical properties of objects together with their attributes and different types of relations between object components.
The proposed multi-hierarchical graphs can represent artefacts being designed at different levels of detail and at different stages of the design process. They allow for hiding unnecessary at the moment low-level data and
Case study
Let us consider an example of a mail delivery robot operating in a multi-storeyed office building. The fragments of layouts of two selected floors of such a building are presented in Fig. 4. The reception of the building is located on the first floor. The floors are accessible through the stairs or the lift. There are several departments in the building, each of them occupies several rooms. Moreover, employees are assigned to rooms.
A 3-hierarchical graph representing the layout from Fig. 4 is
Conclusion
In this paper, the graph-based representation of building layouts with many hierarchies is proposed. This representation encodes the syntactic and semantic knowledge about designed objects and therefore can support both design and engineering systems. The presented formalism allows for specifying the relative importance of different hierarchies, determining relations between fragments of hierarchies and elements of the smart house structure, and for determining the access level to information.
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