Interdisciplinary Conference of the International Society Arts, Mathematics and Architecture

ISAMA ‘99, 7-11 June, 1999 San Sebastian, Spain

ARTIFICIAL INTELLIGENCE IN BUILDING DESIGN Ö. Ciftcioglu*, S. Durmisevic**, E. Durmisevic** and S. Sariyildiz** TU Delft, Faculty of Information Technology and Systems* TU Delft, Faculty of Architecture** Berlageweg 1 2628 CR Delft, The Netherlands fax: ++ 31 15 278 41 27

To comply with the associated requirements for a building design in a consistent and optimal way, careful architectural deliberations have to be carried out before a final decision is made. Due to comprehensive considerations that are necessary, the decision process is very much time consuming. To facilitate such a design process, a systematic approach with the application of artificial intelligence (AI)-based information processing for building design is described. In this approach, a human expertise is cast on knowledge representation in a computer-based system, which is made available to external inputs for human-like decisions in building design. Therefore, the outcome is consistent with the knowledge-base established within the system and the decisions made are instant, compared to comprehensive “human-deliberations”, at large. The AI method used is based on fuzzy logic and neural network as a novel neuro-fuzzy approach in building design, where a neural network is used as a knowledge base providing fuzzy relations between requirements at the input space and design goals at the output space. The paper describes the method together with application to a case study.

Introduction As well as in other sciences, the developments on the information communication technology (ICT) influence Architecture and the associated design processes. But the question that remains open is still to what extend can the architectural design process could be computerized. As Architecture deals with alpha, beta and gamma sciences altogether, the combination of these disciplines makes the Architecture unique. The betamind as a scientist brings together objectively the outside world of the facts of logic with the rational mind culture. The alpha-mind brings as a culture the subjective outside world of the beauty and moral, with the artistic intuitive soul. The combination of these minds makes the approach complete and this completion can be seen in architect. This makes architect a professionally unique, compared with other professionals. Developments on computational intelligence technically make it possible that architect can be supported during the decision making process of the design. A building design involves a number of activities and considerations due to broad knowledge that is necessary from different experts. The communication among them is not straightforward and this slows down the process of mutual decision-makings. This results in delays in decisions, expanding the process over longer period of time. Next to the problem of communication of experts in different fields, there are other important factors hindering the easy process of decision-makings. One of them is the complexity of the building design process. Therefore, the support that is supposedly to come to the aid of decision-making is highly desirable in such a case. Surely, the essence of the building design considerations has many linguistic qualities as well as engineering components. Therefore, the complexity of the problem has diverse dimensions. Presumably, the

engineering considerations are easier to tackle, since the methods of exact sciences are rather well developed. To deal with the linguistic terms of architectural design is not easy task due to the inexactness of the expressions in the sense that the qualities discussed are not physical but rather conceptual. The aid one can think of for the problem should have intelligent capabilities to assist the human considerations. Loosely, we can refer to this aid as decision support system. With respect to design and decision-making processes, design is a brain activity and there are no firm rules to guide the brain activity during this process. Since the AI approaches are based on the activities similar to those used by brain, for logical pattern recognition type decision-making tasks, these approaches are very effective to support the design decision-making. In this work the processing of building design information by means of an AI method, namely neuro-fuzzy approach is described as a neural expert to building design. Since human eventually should evaluate the performance of such tools, they can be deemed as decision support systems. The organization of the paper is as follows. Part 2 gives a brief description of linguistic information processing together and the development of a neuro-fuzzy system to aid building design task providing optimal design solution as an expert, based on AI. Part 3 gives the details of building design information processing for building design decisions. Part 4 describes the implementation with test data and this is followed by conclusions.

Neuro-Fuzzy Approach As the building design is a highly knowledge intensive problem, the most of the modern building design problems are either too complex or too ill defined to analyze with conventional methods. For solution to such problems, fuzzy logic techniques are invoked. By defining the design (functional and technical) requirements as fuzzy sets, one can perform inexact reasoning during the conceptual or creative phase of the design process with optimal information routing and design decisions. Fuzzy set theory was introduced through Zadeh (Zadeh,1965). With fuzzy sets, a numerical value is classified into one or more linguistic labels. These labels may be discrete as well as continuous and they are associated with appropriate fuzzy sets. A fuzzy set A on the universe X is a set defined by a membership function µA representing a mapping µA : X → {0,1} where the value µA(x) for the fuzzy set A is called the membership value of x ∈ X . The membership value can be interpreted as degree of x belonging to the fuzzy set A. In other words, the membership functions represent the numerical strength of linguistic labels for the domain of classification. Since the membership functions can overlap, this results in multi-value representation of the knowledge. An input value intersects with one or more membership functions of the input classification and therefore it is attached to several linguistic labels. Before introducing information to a fuzzy system, the information at hand is fuzzyfied. This is done by an input classification, matching the input value against a chosen set of linguistic labels. These labels partly overlap, so that a numerical value can be classified into more than one label, each with an associated membership value. Since one linguistic value can be attached to several numerical values in different fuzzy sets, it can trigger more than one rule producing several answers. This multiple answer can be combined to reach an optimal decision or a decision region. Fuzzy associative memory (FAM) is a transformation described by Kosko (Kosko,1992). It maps a fuzzy set to another fuzzy set. In general the FAM system includes a bank of different FAM associations. Each association corresponds to a different sequence of considerations that are expressed in numerical form by means of fuzzy logic. Therefore, the numerical data express the membership values connected to the associations. The associations are ordered systematically in a matrix form so that the numerical data constitute a matrix M called FAM matrix . The FAM matrices are separated and they are accessed in parallel. Consider fuzzy sets A and B which are multi-valued or fuzzy subsets of sets X and Y. Therefore A and B are in general

in the form of a sequence of fuzzy values that they are called fuzzy vectors. The components of these vectors can be the membership values corresponding to the linguistic quantities of concern. The relationship between A and B fuzzy vectors is represented by means of FAM matrix and the transformation is performed with an operation similar to classical vector-matrix multiplication. The equivalence of fuzzy sets and radial basis functions (RBF) networks is already identified (Jang,1993). RBF networks are feed-forward neural networks which use radial basis functions in contrast with sigmoidal non-linearity of conventional feed-forward networks. With this feature, in RBF networks the base functions serve to establish the fuzzy relation between input and output space the fuzzy relation being the FAM associations in continuous form although, originally FAM relations are expressed in discrete form by means of a matrix M known as correlation-minimum encoding. Using FAM, information ordering in building design is described before (Sariyildiz et al., 1998). In the present fuzzy-neural approach with radial basis functions, the input output fuzzy relations are considered to be continuous and the establishment of the relations is considered to be as multivariable continuous function approximations. Since the RBF network is central to this research for processing the building information, it is briefly described below.

Multivariable Functional Interpolation We consider a set of N data vectors {xi , i=1,...,N} dimension of p in Rp and N real numbers {di, i=1,2,...,N}. We seek a function f(x): Rp → R1 that satisfies the interpolation conditions f(xi)=di, i=1,2,...N. There are several methods as solutions for this interpolation problem, like Lagrange interpolation functions. Here we consider radial base functions (RBF) due to their suitability for use in the present research. The characteristic feature of radial functions considered here is that their response decreases monotonically with distance from a central point. The RBF approach constructs a linear space using a set of radial basis functions φ(||x-cj||) defined with a norm which is generally Euclidean. The center described with a vector cj, a distance scale and the shape of the radial function are parameters of the model. By means of these base functions, we can model the function as N

f ( x ) = ∑ w j φ ( || x − c j || ) j =1

cj, x ∈ Rp ,

where wj are weights or coefficients. The interpolation conditions f(xi) = di , i=1,2,...N can be generalized as N

f k ( x ) = ∑ w j φ ( || x − c j || )

x ∈ R p , k = 1,..., s

j =1

k=1,2,.....,s. Once where the mapping from input to output is Rp → Rs and fk(xi) = dik , i=1,2,......,p ; the appropriate basis functions (φ) and the distance measure are selected the interpolation function can be established. Among several radial-basis functions, the Gaussian basis function is of particular interest and used in this research:

φ ( r ) = exp( −

r2 ) 2σ 2

While radial basis functions have been used for many years for multivariable interpolation with firm mathematical base, it was only recently that they are introduced for use with neural networks (Broomhead and Lowe, 1988). Therefore, such a structure is coined as radial basis function network. The use with neural network architecture has a number of advantages over the other type of feed-forward neural network architectures with respect to training and locality of approximation. Consequently interest in the network has grown very rapidly and it is now widely used in many diverse applications. Due to their connections to fuzzy logic, radial basis function networks are very suitable for AI applications for linguistic information processing, as this is the concern of the present research as well.

In the present application, for a set of provided building design information the RBF network is "trained" which means, the information given is stored in a neural network where the functional relationships among the input data are structured in the form of input-out relationship. In this form, the neural RBF network serves as a knowledge base for the designer.

Neuro-Fuzzy Application in Building Design In this research we restricted ourselves to the dwelling function in order to demonstrate the potential of the method for application. Firstly, the basic background of the dwellings was provided, indicating the direction for knowledge collection and representation. An apartment building in Amsterdam was chosen as a case study but later on, other apartments were taken into consideration in order to provide the necessary amount of input data for the purpose of a neural network training. The reason for choosing the apartment building in Amsterdam was because there has been a considerable change during the recent reconstruction of this building which significantly improved the building performance and the possibility of the appartments to be transformed and to meet different requirements (fig. 2) (Cuperus,1991). This aspect of flexibility and transformation was the basis for the further research consisting of: data gathering, knowledge-base forming and establishing important design criteria. According to this data, an evaluation model is designed, which provides Transformation Value (∑Tv) that indicates the possibility of an apartment to transform.

Fig. 2: Different layouts were possible within the same construction constraints due to reconstruction, namely installation possitioning and accesibility

The purpose of the whole process is to provide an evaluation of both spatial qualities of an apartment and the structural quality in respect to transformation. It is considered that if combination of Qs and ∑Tv value is greater or less than 0.5 would mean that different action can be undertaken (fig. 3).

Fig. 3: Possible action on the basis of obtained results, in relation to financial justifiability

Dweling Analyses A dwelling has to accommodate both functional and structural requirements. Both of them consist of subdivisions, whose interdependency determines the flexibility of a dwelling or in other words its capacity to transform. The functional requirements provide an information regarding the spatial quality (Qs – value) of an apartment. On the other hand, the structural parameters provide more information on structural suitability in relation to the transformation possibilities of an apartment (∑Tv – value). More detailed representation of criteria for obtaining Qs and ∑Tv values are given in the (fig. 4).

Functional Requirements for a Dwelling Each dwelling should satisfy sleeping, living and servicing requirements, which includes at least one: entrance, main hall, internal hall, living room, kitchen, dining room, one bedroom, WC and bathroom. Additional elements can be: working station, hobby room, separate wardrobe, balcony and lodge, sauna, exercise room and guest rooms. We will restrict research domain only to primary functional requirements and their interrelationships. The combination of the following three aspects will provide a Qs value (organizational quality of an apartment). a. connection values b. orientation values and natural lighting c. number of residents per m2 (Neufert, 1998) Each of the above mentioned aspects is graded separately. In first instance, the grading scale is defined and than accordingly each deliberated apartment variant was graded on the basis of established grading system. Important remark is that in this case, the Qs value was provided by simple computation, and was not used for neural network training.

Defining Structural Requirements In order to define technical flexibility of a dwelling, all its elements will be classified into two groups: fixed and flexible. This is necessary when defining the transformation capacity of the structure. Fixed Elements Under the fixed elements the following aspects are considered: a. load bearing structure (support) a.1. type and dimension values a.2. type and material values (Tv1 value is obtained through consideration of a.1 and a.2). When discussing load bearing structure the following aspects are of an importance: materials, dimension (span) and type of structure. Interdependence of the dimensions and types influences the spatial flexibility, while the interdependence of the materials and types can influence the capacity of structure to be transformed and therefore the spatial flexibility as well. In this paper following types are distinguished: tunnel (T), scelet (S), panel (P) and the combination (C). Regarding materials, very rough distinction is made, meaning that only poured concrete (as a material that is difficult to tear down and replace) and blocks (all other materials, which are easier to tear down and replace) are considered. b. vertical installations b.1. positioning - central or peripheral positioning. b.2. accessibility - build in construction or independent of construction (Tv2 value is obtained through consideration of b.1 and b.2).

Flexible Elements Under flexible elements the following aspects were considered: a. inside partitioning The materialization of the walls in the apartment and the possibility to remove them, or change their position depends greatly on the fact whether they are made of masonry or system walls. b. installation servicing – horizontal and vertical distribution In this context the accessibility and positioning were taken into consideration, such as for example, whether the installation servicing is build in construction or separated from it These two aspects (“a” and “b”) are the most important determining factors for the layout flexibility. Today we can talk of having inside partitioning and installation servicing as being separate from the main construction, while in the past this was not a case, which made buildings very difficult to adapt to the new requirements. Whether the vertical installations on a building level and servicing distribution on a dwelling level are either build in construction or separated from construction, influences greatly the transformation value. All above-mentioned parameters that were used to evaluate the structural and spatial flexibility are generated in the evaluation model. This model provides a ∑Tv - transformation value (fig. 4). The elements used for the network training are shown in this figure as well. ∑Tv is obtained by simple computation involving Tv values.

Fig. 4: symbolic representation: (FR) functional requirement, (SR) structural requirement, (F) function, (Fix) fixed elements, (Flex) flexible elements, (Ca) capacity, (Co) conection values, (Or) orientation, (LB) loadbearing, (VI) vertival installations, (IP) inside partitioning, (IS) installation serviceing, (TD) type-dimension, (TM) type-material, (Acc) accesibility, (Pos) positioning, (ST) spatial transformation, (Qs) spatial quality, (Tv1-4) obtained transformation valuse, (∑Tv) final transormation value

Method Evaluation For the evaluation of the method Transformation Value (∑Tv) is considered that indicates the possibility of an apartment to transform. For the purpose of a neural network training that is knowledge base forming, 22 design cases for different apartments were provided, which proved to be enough for a rough estimation of the transformation value for any given new apartment subject to probable transformation. For the input, a data base matrix dimensions of p×N [6x22] and for the output a data-base matrix dimensions of s×N [4x22] were used. Six numbers at the input as a row represent the structural parameters, which are important to judge structural flexibility. The four numbers at the output as a row represent Tv1, Tv2, Tv3, and Tv4 values respectively. Transformation Value (∑Tv) is obtained through the computation of the mean of above mentioned four values that it indicates the possibility of an apartment to be transformed, on a scale from 0.0 to 1.0. After the network was trained an arbitrary apartment was taken as a test case, and simply by giving the relevant input values, the transformation value estimate was obtained by the network. The results are shown in fig. 5. Note that figure contains 23 output set while each set has four points. Here 23-rd set is the outcome of the test data which were not seen before by the network. All outcomes (i.e., training and test) are shown together for the sake of the convenience of the evaluations in perspective. However, the test set is also given separately for the explicit representation of the outcomes estimated by the network. The transformation value estimate was found to be sufficiently close to the true value both being equal to 0.4 (estimated 0.41 against the true value 0.39). The result indicated that the network was duly trained and it was able to provide satisfactory results. Naturally, by training the network with more data, or in other words with more design information, would reduce the estimation error, making it more accurate. For the present case, the error is acceptable because it does not effect the final decision based on the outcome. For the purpose of explaining this method we considered 22 different design variants making the case study simple for presentation. design & estimate 1 0.5 0 1

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Fig. 5: Estimations for bulding design data by neuro-fuzzy approach. First 22 set of points are the results of training and the last set (4 points) are the test results. The true values are indicated by circles The estimated value 0.4 (i.e., ∑Tv < 0.5), in the present context means that the transformation of an apartment would be costly, and therefore would be better to keep a “status quo” situation, since the Qs > 0.5, and therefore satisfactory for the given requirement (reference to the fig.3).

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Fig. 6a,b: An arbitrary apartment that is used to test the performance of the network (6a) and representation of the results obtained from test data (6b) where four estimations correspond to the data set 23(last) in fig. 5. During the research on the inputs for the dwelling function, many other aspects that also play an important role in evaluating a possibility of an apartment to transform became evident, but only some were taken into consideration and more worked out in order to get a rough estimation for the ∑Tv value. It is therefore, for more exact (Tv) values the refinement of the whole model will be achieved.

Conclusions Multidisciplinary and multidimensional features of building design information make the design decisions a complex process. Multidimensionality includes also the linguistic qualities to be integrated to the design process and therefore requires a special technique to be used. In this research, neuro-fuzzy AI-based information processing is implemented. The knowledge base is established in a feed-forward neural network structure and it is used for optimal building design decisions. Testing the performance of the approach using actual building design data, as a real design case study, yielded satisfactory design solutions. Although the knowledge-base is formed by rather moderate amount of design information available, the test results clearly indicated the high design potential of the method for cases with complex building design data of much higher volume and dimensions. For improved performance in design and effectiveness in design decisions, the results also evoked the application oriented possibility of integration of the neuro-fuzzy knowledge base into comprehensive building design decision support systems with AI, namely building expert systems.

References: Broomhead, D.S. and D. Lowe (1988). Multivariable Functional Interpolation and Adaptive Networks, Complex Systems, 2, pp. 321-355 Cuperus Y.J., Kaptijns J.H.M., (1991), Niveaugericht Beheer in de Naoorlogse Wijken – Een Open Bouwen Studie in Den Haag Zuidwest,  Werkgroep OBOM, the Nethederlands (in Dutch) Kosko, B. (1992), Neural Networks and Fuzzy Systems, Prentice Hall, Englewood Cliffs, New Jersey Neufert E., (1998), The Handbook of Building Types – Neufert Architect’s Data. Second (International) English Edition, 1998 Reprinted Blackwell Science, 1980 by Blackwell Science Ltd. Roger Jang J.-S and C. –T. Sun (1993), Functional Equivalence Between Radial base Function Networks and Fuzzy Inference Systems, IEEE Trans. on Neural Networks, Vol.4, No.1, January S. Sariyildiz, P. v.d.Veer and Ö. Ciftcioglu (1998), Information Ordering for Decision Support in Building Design, D & DSS, Design & Decision Support Systems, 4th International Conference on Design and Decision Support Systems in Architecture and Urban Planning , Castle Vaeshartelt, Maastricht, July 26-29 Zadeh, L.A., (1965), Fuzzy sets. Information and Control 8, pp.338-353