Fuzzy Logic in Architectural Design - EUSFLAT
Fuzzy Logic in Architectural Design 0.Ciftcioglu and S. Durmisevic TU Delji, Faculty of Architecture, Building Technology, Berlagmeg I , 2628 CR Delji, The Netherlands tel: ++31 15 278 44 85;far: ++31 15 278 41 27; e-mail: o.cificio.~lu@,bk.tudelft.nl Abstract Architecture is a multidisciplinary science with many dimensions. For a design task the major part of the design requirements are often qualitative (soft) next to quantitative design data so that some appropriate information processing tools borrowed from A1 technology must be invoked for rapid and effective treatment. At this point, fuzzy logic can play important role. The research focuses on to identify a fuzzy model of an architectural design and establish the relative importance of the design variables in a design task by means of sensitivity analysis together with validation. Keywords: Fuzzy Logic, Architectural Design, RBF Networks
1
Introduction
Architecture is a multidisciplinary science with many dimensions. Therefore for a successful design there should be a rich collection of information from all relevant disciplines. In this case the ordering of this information and also modeling it in the form of a knowledge base are two important issues. Although abstract mathematics is widely exercised in Architecture, referring to multidisciplinary nature of the design information, such information is not exhaustively treated in design and in most cases design decisions based on the available information relied on the experience and intuition of architect. There are several fundamental reasons for this. In essence, the problem stems from the ill-conditioned nature of design tasks, that is, the architectural design information generally is not convenient to be dealt
with conventional analytical computation and design methods borrowed from other disciplines. One reason is that major part of the design requirements is ofien qualitative (soft) next to quantitative design data. Another reason is the nature of the task, which may be combinatorial and discrete. In the last decade algorithms are being developed which are particularly suitable for such non-analytical design problems. Such methods are collectively referred to as sofi computing [I]. Although artificial intelligence more than a decade is applied to Architecture by means of expert systems, the soft computing methods involving fuzzy logic is not commonly established in this discipline and therefore the associated technology is still not enough exploited in this discipline. However soft computing technology is essential for Architecture since it can deal with 'soft7data,which constitute the major source of architectural information. In this respect, fuzzy logic is appealing technology as following examples will clearly indicate. One example area is building design, which is one of the major activities in architecture and it involves a number of considerations and components. These include the persons in charge for the realisation as well as the peoplehodies concerned with respect to their due involvement and the materials used during the construction. In such a case, the information demand and correspondingly information supply can be immense where information itself may be soft as well so that some appropriate information processing tools borrowed from A1 technology, must be invoked for appropriate and effective treatment. At this point, fuzzy logic can play important role. Another example can be stated in the following way. Architecture is a science where most things can be learned from previous examples and from the successes and failures of previous designs, applying the already known or inventing some new techniques. In other words design
is evolving, according to requirements of specific time, available technology, existing knowledge and personal ability of a designer to combine all these features into a new, evolved design. This implies that the designer should be able to derive from each previous design some qualitative values, especially on customer approval regarding building quality as to assure a successful design. It is interesting to note that on a far larger scale, the success of any customer oriented organization, greatly depends on this particular aspect as well, meaning that the feedback from a customer is quite important for innovation and learning process, both for organization and individual. From this viewpoint, knowledge modeling and management is one of the essential concerns in architecture. For this purpose, fuzzy modeling can be an important concern.
2
Fuzzy modeling
The method of fuzzy modelling applied in this research, in basic mathematical terms can be described as follows. If we assume that the input vector x(t) represents a n-dimensional vector of real-valued fuzzy membership grades: x(t) E [0,1In,then, the output y(t)
of the model represents an m-dimensional vector of corresponding real-valued membership grades, y(t) E [0, 11". This structure actually performs a nonlinear mapping from an n-dimensional hypercube In=[O,11" to an m-dimensional hypercube Im=[O,l]" :
In the actual implementation, xi(t) (i=1,2,.. .,n) in x(t) represents the degree to which an input fuzzy variable xil(t) belongs to a fuzzy set, while yj(t) (j=1,2,. ..,m) in y(t) represents a degree to which an output fuzzy variable yj1(t)belongs to a fuzzy set. To carry out the mapping a radial basis functions (RBF) network and special machine learning technique known as orthogonal least squares (OLS) [3] is used. Such a network with its inherent fuzzy logic based inference system, knowledge base after OLS-based training and input-output, forms an intelligent expert system where the basis functions play the role of membership functions describing the fuzzy sets. There are two aspects in the output space, which are safety and comfort. These two items have their progressive subcomponents. The input aspects, which are identified to be related to safety are given in table I and those related to comfort are given in table 2 [3].
Table 1:Aspects related to safety (15 aspects). Overview
Escape
Lighting
Presence of People
Entrance
Possibilities
Entrance
Public control
Train platform
Distances
Train platform
Few people daytime Few people night
Metro platform
Metro platform
Exchange area
Exchange area
Safety Surrounding Safety in surrounding
Dark areas
Table 2: Aspects related to comfort (28 aspects) Attractiveness Colour Material Spatial proportions Furniture Maintenance
W ayfinding
To the station In station Placement of signs Number of signs
Daylight Pleasantness Orientation
Physiological Noise Temperature winter Temperature summer Draft entrance Draft platforms
Spaciousness entrance
Draft exchange areas
Spaciousness train platform
Ventilation entrance
Spaciousness metro platform
Ventilation platforms
Platform length Platform width Platform height Pleasantness entrance Pleasantness train platform Pleasantness metro platform
The relevant data are obtained from a questionnaire filled in by users. Main purpose of the questionnaire was to provide information on user's perception regarding specific spatial characteristics of the station Blaak in Rotterdam in the Netherlands and to find out to what extend they contribute to ones having the feeling of safety and comfort while at that station. The questions covered all aspects given in table 1 and table 2 and additional two final questions were related to user's perception of public safety and comfort at stations. The trained RBF network outcomes are shown infigure 1 for comfort parameter where RBF network has 43 input variables, two output variables (comfort and safety) and 196 training cases.
Figure 1 : Network training results for comfort variable with 90 receptive fields, 43 inputs, two outputs and 196 cases. Broken lines represent the knowledge model response to the training data after training.
3
Sensitivity analysis
To identify the graded importance of the input design variables for each output we define the sensitivity S as
which indicates that the sensitivity is a function of the input pattern vector x, for each case. Therefore an averaging process over the pattern vectors can carry out the final sensitivity computation:
N is the number of pattern vectors and equal to 196, for this case. Finally, the sensitivity vector as counterpart of the common pattern vector can be normalized to unity length. This vector is called priority vector since each vector component indicates the priority of the corresponding input variable in the design process. The magnitude of each vector component is shown in figure 2 for both output variables (comfort and safety). Due to averaging process, the assessment of the accuracy of the sensitivity analysis carried out above is validated by means of eigenvector method (EVM) which is developed by Saaty [4,5]. In this method, the n x n matrix, which is termed as the reciprocal judgement matrix (RJM), is obtained by arranging the pairwise comparison ratios. The EVM compute the priority vector, ranking the relative importance of factors being compared. In this work, the relative importance factors and the corresponding basic RJM is determined by means of pair wise ratio of the sensitivities computed in each case.
.
-US!
- -
v c w i
->-
-.-1. . -
,,
: I
The comparison of figures 2 and 3 reveals that the difference is insignificant and common sensitivity analysis is accurate enough for priority determination for the architectural design variables.
4 Conclusions
sensitivity analysis of 43 input aspects for comfort (a); for safety (b) The composite RJM is determined by element-wise averaging the basic judgment matrices, which are altogether 196, in this case. In the EVM the inconsistency or imprecision in the judgement ratios and eventually in the RJM do not have significant effect on the priority vector, which is the orthonormal eigenvector of the largest eigenvalue of the composite RJM. Therefore it yields the accurate gradation of the relative sensitivities of the fuzzy model being considered thereby provides a means to assess the performance of the common sensitivity analysis. The results of EVM analysis is shown in finure 3.
Fuzzy logic is integrated to Architectural design for knowledge modeling and the priority ranking of the design variables. The fuzzy model is established by a radial basis function network. The priority ranking is determined by sensitivity analysis using the model established and the results are validated in the sense of accuracy of the results as well as in the sense of architectural design considerations. In Architecture, the input and output space dimensions of the model can be very high in contrast to engineering systems. This is one of the essential points that machine learning is most appropriate for fuzzy logic in Architecture for knowledge model identification. This makes fuzzy logic approach special and at the same time relatively complex in this particular domain. However, in return to this important substantiation in design is achieved.
References [l] Jang J.S., Sun C.T. and Mizutani E., (1997), Fuzzy-Neuro and Soft Computing, Prentice-Hall International, Inc., Upper saddle River, NJ 07458, [2] Chen S, C.F.N. Cowan and Grant, P.M. (1991). Orthogonal least squares algorithm for radial basis functions network, IEEE Trans. on Neural Networks, Vo1.2, No.2, pp.302-309, March [3] Durmisevic, S., Ciftcioglu, 0. and Sariyildiz, S. (2000). An application of neural network in postoccupancy evaluation of underground stations. Proc. International Conference on Construction and Information Technology (CIT 2000). Icelandic Building Research Institute, pp,3 10-320 Reykjavik, Iceland. June 28-30 [4] Saaty, T.L. (1980), The Analytic Hierarchy Process, Mc-Graw-Hill, New York
Figure 3. Priority of the design variables from the eigen vector method using 43 input aspects for comfort (a); for safety (b)
[5] Saaty T.L. (2000), The Brain: Unraveling the Mystery of How It Works, RWS Publications, Pittsburgh, PA 15213
1
Introduction
Architecture is a multidisciplinary science with many dimensions. Therefore for a successful design there should be a rich collection of information from all relevant disciplines. In this case the ordering of this information and also modeling it in the form of a knowledge base are two important issues. Although abstract mathematics is widely exercised in Architecture, referring to multidisciplinary nature of the design information, such information is not exhaustively treated in design and in most cases design decisions based on the available information relied on the experience and intuition of architect. There are several fundamental reasons for this. In essence, the problem stems from the ill-conditioned nature of design tasks, that is, the architectural design information generally is not convenient to be dealt
with conventional analytical computation and design methods borrowed from other disciplines. One reason is that major part of the design requirements is ofien qualitative (soft) next to quantitative design data. Another reason is the nature of the task, which may be combinatorial and discrete. In the last decade algorithms are being developed which are particularly suitable for such non-analytical design problems. Such methods are collectively referred to as sofi computing [I]. Although artificial intelligence more than a decade is applied to Architecture by means of expert systems, the soft computing methods involving fuzzy logic is not commonly established in this discipline and therefore the associated technology is still not enough exploited in this discipline. However soft computing technology is essential for Architecture since it can deal with 'soft7data,which constitute the major source of architectural information. In this respect, fuzzy logic is appealing technology as following examples will clearly indicate. One example area is building design, which is one of the major activities in architecture and it involves a number of considerations and components. These include the persons in charge for the realisation as well as the peoplehodies concerned with respect to their due involvement and the materials used during the construction. In such a case, the information demand and correspondingly information supply can be immense where information itself may be soft as well so that some appropriate information processing tools borrowed from A1 technology, must be invoked for appropriate and effective treatment. At this point, fuzzy logic can play important role. Another example can be stated in the following way. Architecture is a science where most things can be learned from previous examples and from the successes and failures of previous designs, applying the already known or inventing some new techniques. In other words design
is evolving, according to requirements of specific time, available technology, existing knowledge and personal ability of a designer to combine all these features into a new, evolved design. This implies that the designer should be able to derive from each previous design some qualitative values, especially on customer approval regarding building quality as to assure a successful design. It is interesting to note that on a far larger scale, the success of any customer oriented organization, greatly depends on this particular aspect as well, meaning that the feedback from a customer is quite important for innovation and learning process, both for organization and individual. From this viewpoint, knowledge modeling and management is one of the essential concerns in architecture. For this purpose, fuzzy modeling can be an important concern.
2
Fuzzy modeling
The method of fuzzy modelling applied in this research, in basic mathematical terms can be described as follows. If we assume that the input vector x(t) represents a n-dimensional vector of real-valued fuzzy membership grades: x(t) E [0,1In,then, the output y(t)
of the model represents an m-dimensional vector of corresponding real-valued membership grades, y(t) E [0, 11". This structure actually performs a nonlinear mapping from an n-dimensional hypercube In=[O,11" to an m-dimensional hypercube Im=[O,l]" :
In the actual implementation, xi(t) (i=1,2,.. .,n) in x(t) represents the degree to which an input fuzzy variable xil(t) belongs to a fuzzy set, while yj(t) (j=1,2,. ..,m) in y(t) represents a degree to which an output fuzzy variable yj1(t)belongs to a fuzzy set. To carry out the mapping a radial basis functions (RBF) network and special machine learning technique known as orthogonal least squares (OLS) [3] is used. Such a network with its inherent fuzzy logic based inference system, knowledge base after OLS-based training and input-output, forms an intelligent expert system where the basis functions play the role of membership functions describing the fuzzy sets. There are two aspects in the output space, which are safety and comfort. These two items have their progressive subcomponents. The input aspects, which are identified to be related to safety are given in table I and those related to comfort are given in table 2 [3].
Table 1:Aspects related to safety (15 aspects). Overview
Escape
Lighting
Presence of People
Entrance
Possibilities
Entrance
Public control
Train platform
Distances
Train platform
Few people daytime Few people night
Metro platform
Metro platform
Exchange area
Exchange area
Safety Surrounding Safety in surrounding
Dark areas
Table 2: Aspects related to comfort (28 aspects) Attractiveness Colour Material Spatial proportions Furniture Maintenance
W ayfinding
To the station In station Placement of signs Number of signs
Daylight Pleasantness Orientation
Physiological Noise Temperature winter Temperature summer Draft entrance Draft platforms
Spaciousness entrance
Draft exchange areas
Spaciousness train platform
Ventilation entrance
Spaciousness metro platform
Ventilation platforms
Platform length Platform width Platform height Pleasantness entrance Pleasantness train platform Pleasantness metro platform
The relevant data are obtained from a questionnaire filled in by users. Main purpose of the questionnaire was to provide information on user's perception regarding specific spatial characteristics of the station Blaak in Rotterdam in the Netherlands and to find out to what extend they contribute to ones having the feeling of safety and comfort while at that station. The questions covered all aspects given in table 1 and table 2 and additional two final questions were related to user's perception of public safety and comfort at stations. The trained RBF network outcomes are shown infigure 1 for comfort parameter where RBF network has 43 input variables, two output variables (comfort and safety) and 196 training cases.
Figure 1 : Network training results for comfort variable with 90 receptive fields, 43 inputs, two outputs and 196 cases. Broken lines represent the knowledge model response to the training data after training.
3
Sensitivity analysis
To identify the graded importance of the input design variables for each output we define the sensitivity S as
which indicates that the sensitivity is a function of the input pattern vector x, for each case. Therefore an averaging process over the pattern vectors can carry out the final sensitivity computation:
N is the number of pattern vectors and equal to 196, for this case. Finally, the sensitivity vector as counterpart of the common pattern vector can be normalized to unity length. This vector is called priority vector since each vector component indicates the priority of the corresponding input variable in the design process. The magnitude of each vector component is shown in figure 2 for both output variables (comfort and safety). Due to averaging process, the assessment of the accuracy of the sensitivity analysis carried out above is validated by means of eigenvector method (EVM) which is developed by Saaty [4,5]. In this method, the n x n matrix, which is termed as the reciprocal judgement matrix (RJM), is obtained by arranging the pairwise comparison ratios. The EVM compute the priority vector, ranking the relative importance of factors being compared. In this work, the relative importance factors and the corresponding basic RJM is determined by means of pair wise ratio of the sensitivities computed in each case.
.
-US!
- -
v c w i
->-
-.-1. . -
,,
: I
The comparison of figures 2 and 3 reveals that the difference is insignificant and common sensitivity analysis is accurate enough for priority determination for the architectural design variables.
4 Conclusions
sensitivity analysis of 43 input aspects for comfort (a); for safety (b) The composite RJM is determined by element-wise averaging the basic judgment matrices, which are altogether 196, in this case. In the EVM the inconsistency or imprecision in the judgement ratios and eventually in the RJM do not have significant effect on the priority vector, which is the orthonormal eigenvector of the largest eigenvalue of the composite RJM. Therefore it yields the accurate gradation of the relative sensitivities of the fuzzy model being considered thereby provides a means to assess the performance of the common sensitivity analysis. The results of EVM analysis is shown in finure 3.
Fuzzy logic is integrated to Architectural design for knowledge modeling and the priority ranking of the design variables. The fuzzy model is established by a radial basis function network. The priority ranking is determined by sensitivity analysis using the model established and the results are validated in the sense of accuracy of the results as well as in the sense of architectural design considerations. In Architecture, the input and output space dimensions of the model can be very high in contrast to engineering systems. This is one of the essential points that machine learning is most appropriate for fuzzy logic in Architecture for knowledge model identification. This makes fuzzy logic approach special and at the same time relatively complex in this particular domain. However, in return to this important substantiation in design is achieved.
References [l] Jang J.S., Sun C.T. and Mizutani E., (1997), Fuzzy-Neuro and Soft Computing, Prentice-Hall International, Inc., Upper saddle River, NJ 07458, [2] Chen S, C.F.N. Cowan and Grant, P.M. (1991). Orthogonal least squares algorithm for radial basis functions network, IEEE Trans. on Neural Networks, Vo1.2, No.2, pp.302-309, March [3] Durmisevic, S., Ciftcioglu, 0. and Sariyildiz, S. (2000). An application of neural network in postoccupancy evaluation of underground stations. Proc. International Conference on Construction and Information Technology (CIT 2000). Icelandic Building Research Institute, pp,3 10-320 Reykjavik, Iceland. June 28-30 [4] Saaty, T.L. (1980), The Analytic Hierarchy Process, Mc-Graw-Hill, New York
Figure 3. Priority of the design variables from the eigen vector method using 43 input aspects for comfort (a); for safety (b)
[5] Saaty T.L. (2000), The Brain: Unraveling the Mystery of How It Works, RWS Publications, Pittsburgh, PA 15213
