Chapter 3 Schematic Design of Case Representation
3.3 Schematic Attribute Property
The requirement of design can be classified to interior requirement and exterior requirement; for exterior requirement, physical environment (e.g., wind, sun light) and the interaction between space and environment (e.g., view, noise) are needed to consider. For interior requirement, the consideration will change according to different construction types (i.e., the space design of residence house and building are different), we will discuss the requirement of residence in this section.
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1. External (environment)
(1) Uniformity : no direct facing can be divided to light and wind (i) Light, i.e., when there is only one window open up inside a room, it will produce glare phenomena (ii) Wind, i.e., Draft occurs when the entry and exit of room (door or window) are aligned.
(2) Orientation : there are absolution and none absolution direction (i) Absolution direction :
Light, i.e., room with a western exposure.
Wind, i.e., northeasterly season wind.
(ii) None Absolution direction, e.g., view, noise, etc.
2. Internal (Design required of small house)
(1) The sequence of syntactic, i.e., It is not advisory to have kitchen ahead of bedroom.
(2) Size of entrance. Places after the main entrance must only be vestibule, living room or porch.
(3) Room inside room is prohibited, i.e., Study room in the bedroom.
(4) Not more than one door in a room (closed space).
(5) Toilet should not exist in the kitchen.
(6) Toilet is prohibited to face directly with master bedroom.
(7) Not advisory to place toilet just beside master bedroom door.
(8) Gas stove is placed near window.
(9) Bedroom area can not be larger than living room.
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3. Degree of space privacy
Degree of space privacy can be divided into 4 categories (1) Open, e.g., living room, tunnel, etc.
(2) Semi open, e.g., dining room, kitchen, etc.
(3) Semi private, e.g., intermediate space.
(4) Private, e.g., bed room, study room, toile, etc.
Based on the degree of space privacy, the sequence of space is Open area >
semi open > semi private> private.
As shown in Figure 3.6, we can use cognitive map [14] to indicate the relation of requirement including limit of design and requirements.
Figure 3.6 The limitation and requirement of design
3.4 Schematic Attribute Property
As mentioned above, we represent case in 3 layers including location/section, building type, configuration, where each layer can be divided to 3 views including
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usage, topology and constraint rule as shown in Figure 3.7. We focus on schematic design here and only the usage of the design of view of layer1 and layer2 will be discussed.
Figure 3.7 The traditional design using our propose model
Definition 3.1 Case in a three-tuple
Hierarchical CBR Structure, HCBR ={L, N, R}, where 1. L = {layer1, layer2, …, layern} is a point of view.
2. N={node1, node2,…,noden} is a member of layer.
3. R={HP}, HP includes relations “Has-Part”.
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Figure 3.8 A case of HCBR
(1) Layer (L)
Layer 1 : Site characteristic level, i.e., layer1 in Figure 3.7 : location /section which explains the degree of site usage and important information of layer 2 and layer 3 respectively.
Layer 2 : Building level, i.e., layer2 in Figure 3.7 : building type which explains the types of building, containment of space, etc.
Layer 3 : Room level , i.e., layer3 in Figure 3.7 : Configuration which explains the characteristic of each room, e.g., area scale, external requirement.
(2) Node (N)
Each node expressed by frame knowledge is an object coming after instance, based on the consideration of extension; we have ontology to explain category that can produce object. The ontology owns “a-kind-of”
and “IS-A” relationships between the classes of comparison in future [1].
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Figure 3.9 The mapping between frame and ontology
Table 3.1 The data types of case
Algorithm 3.1 Ontology-to-Frame Algorithm Input: Input related ontology according to layer.
Output: Frame
Step 1. List the knowledge case set for the ontology, ontology knowledge classes contained classes, and relationship.
Step 2. Choose related attribute according to requirement.
Step 3. Copy attributes to frame slot.
Step 4. Fill in suitable rule to frame.
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(3) Edge (E): Has-part. Currently, we only have one type of relationship between frames.
Detailed explanation for each layer is listed below:
Layer 1 : Site characteristic Layer
The main function of site characteristic layer is to describe the location as shown in Figure 3.10; besides, information of layer2 and layer3 are also included e.g. space arrangement, squire size. Therefore, information can be completely received and compared when searching on first stage, required property of first stage are listed below.
(1) The character of base, e.g., zone.
(2) The intensity of usage, e.g., Building Bulk Ratio, Coverage Ratio, etc.
(3) The construction style, e.g., house, office building, etc.
(4) The space arrangement, e.g., 2 x Bedroom and 1 x Living room, (5) The square size
(6) The using floor
Figure 3.10 The site ontology
Layer 2 : Building Layer
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This stage is mainly explaining the classification of architectural building as shown in Figure 3.11, the required property of stage 2 is listed below.
(1) The construction style, e.g., house, office building, etc.
(2) The space arrangement, e.g., 2 x Bedroom and 1 x Living room.
(3) The square size and using floor
(4) The construction character = (E, V, M, R, L, C, P, I, G)
The main explanations of construction character are showed in Table 3.2.
Table 3.2 The construction characteristic of building
Tag Construction character
Description
E Elevator Elevator inside residence, usually for vertical transportation.
V View Generally 5 floor above possess
enough view.
M Mixed space used Application of space function, i.e., living room, dining room, bed room are sharing same space.
R Complex residence Numbers of residence family in same story.
L Low complexity activity
The complexity of people coming in/
going out of residence space.
C Cross maisonette Intermediate layer room and floor in the floor, usually for height raising space.
P Parking Parking space, usually in basement.
I Infrastructure Service type of facility, e.g., swimming pool.
G Guard Safety guard.
In Table 3.3, the characteristic of different construction types are explained, i.e., town house contains the characteristic of low complexity activity and infrastructure required.
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Table 3.3 The look up Table of building characteristic
(5) The view direction (6) The noise direction
Figure 3.11 The building ontology
Layer 3 : Room Layer
This stage is applied mainly to describe the configuration of space, Figure 3.13, describes the characteristic of each space and the relations of spatial connection. The required property of stage 3 is listed below.
(1) The name of space (2) The area size
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(3) The private level
(4) The space required, e.g., view, wind, etc.
(5) The space refuse, e.g., noise.
(6) The relation type = (C, D, A, P, I), Space connection rule can be divided into different types as below.
Table 3.4 The relation type of space
Tag Type Descript
C Connection Direct connection characteristic between spaces, i.e., master bed room will connect with a bath room space.
D Disconnection
Disconnection characteristic between spaces, i.e., dining room will not connect with toilet.
A Adjacency
Adjacency characteristic, e.g., living room, dining room and kitchen will be adjacent to each others.
P Dependence
Possess a visible requirement but can not reach directly, i.e., living room needs a view, so it needs to face towards park.
I Independence
Possess an invisible requirement and also cannot reach directly, i.e., avoid from noise, living room doesn’t need to face towards road.
Definition 3.2 Adjacency matrix
The adjacency matrix of a finite directed graph G on n vertices is the n × n matrix where the nondiagonal entry aijis the number of edges from vertex i to vertex j, and the diagonal entry aiiis either twice the number of loops at vertex i or just the number of loops. There exists a unique adjacency matrix for each graph, and it is not the adjacency matrix of any other graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. (Reference from WIKI)
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Figure 3.12 An example of label graph and adjacency matrix
(7) The center coordinate
(8) The relative distance to center coordinate of house
Figure 3.13 The room ontology
Detailed explanation of node is listed below:
Frame-Based Knowledge Representation
Frame-Based Knowledge Representation proposed by Mawin Minsky in 1975 is primarily used to develop new specialist system. Frame-Based Knowledge Representation mainly consisting of frame name, relations between frames, slot value, default slot value, slot value area/field, and procedure information (Negnevitsky, 2002) is used to describe our knowledge.
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Table 3.5 The components of frame
Component Description
Frame name
After area knowledge is divided by specialist into each knowledge frame, the knowledge behind each frame will be named and each knowledge frame is representative of the sub-area knowledge consisted in that area.
Relations between frames
Describe the relation between knowledge frames, i.e., inheritage relations between parents & sub-group, and relations between frame of the same level and interaction between knowledge frames based on the relations.
Slot value
Each knowledge frame contains one or more properties, when processing to certain property, data are filled (categorized) to that property. Symbols, numbers and Boolean can be used to represent slot value.
Default slot value
Under start-up condition or default condition of property that yet to be inferred, default slot value is used for operation.
Slot value area Appropriate /probable area is set based on data properties.
Procedure information
When system is processing inference, it will meet with either of the two cases as below:
(i) When changed: Related inference rules will be processed when slot value changes.
(ii) When needed: Related inference rules will be processed when certain requirement, conditions and data are needed.
From the Table above, we know that frame name which is the same as category name contains its properties and methods. When inference is processed, knowledge frames will not affect each other but operate independently. From the interaction between frames, information can be transferred between frames are possible, and the description of relations between frames, is similar with interaction among the same level and inheritance relation between different levels.
Therefore, we know that frame-based Knowledge Representation has the properties of object encapsulation and inheritance. In AI (Artificial Intelligence) area, this Representative method is also termed as object knowledge representative method. So far both represent the same method.
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Figure 3.14 The characteristic of frame
Finally, we can use a simple example to explain our mode, as shown in Figure 3.15.
Figure 3.15 An example of HCBR
Evaluation
After modeling the architectural plans knowledge, we can evaluate them in terms of different aspects, which included expressive power, the extensibility and operative. HCBR is a hierarchical CBR framework, which is the method commonly used by expert system, and has good performance on expressive power, as shown in Table 3.6. The performance of extensibility is built up hierarchical;
therefore the extension of layer is very flexible and also possess acceptable performance on the extension of frame attribute, as shown in Table 3.7.
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Eventually, based on the operative, algorithm and method can be embedded to attribute and infer through trigger due to the inference ability of the frame.
Table 3.6 The expressive Power
Table 3.7 The extensibility
As a comprehensive view, our model is a knowledge model represented by ontology-based method, so that it can have well performance on knowledge description, flexibility of extension and inference.
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Chapter 4 Hierarchical CBR Schematic Design (HCBRSD)
4.1 CBR Support Exam Item Design
The Hierarchical CBR Schematic Design is based on CBR framework [4]
[18] [19], and the structure of frames is used to express knowledge. This can be a kind of object inheritance, and also can be used for derivation, so it is widely used by experts. From system operation of CBR structure, requirements are first set and relevant floor plans are taken out from data storage. After that, the system will retrieve several of the floor plans, called case retrieval. The user chooses to use tools provided by system to facilitate changes, is called case adaptation (include case reuse and case revise) and finally, adapted file will be set as exam paper and stored in data storage again, which is termed as case retain.
Figure 4.1 The hierarchical CBR schematic design
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4.2 Case Retrieval
In the similar appraisal's situation, the system will obtain the preliminary detailed list case that is similar to the new question in the case storehouse. In this detailed list's situation, the arrangement will exist in the range of the similar score. If in the similarity grading past situation's threshold value, this case will be removed from the name list. Then, the system or the user may decide that in this kind of situation, is most similar and the best for further analysis.
Reminder is a key component of analogical reasoning through cases: in other words, a person or computer must be reminded of the appropriate case at the right time (Tsatsoulis and Williams, 2000). Retrieval is an action to recall a case in CBR. By retrieving a case from memory, a CBR system must decide which is the most appropriate case for current status based on the comparison of the degree of similarity. Therefore, the recall cases are dominated by similarity assessment and retrieval will be greatly influenced by the way the case is organized.
4.2.1 Similarity function
Similarity is used when indicating a connection between two objects [16].
Designers always compare the similarity of architectural elements to solve design problem as well as generate ideas during design process. For example, in the case of the Frank House designed by Peter Eisenman, the idea of “layering” comes from the similar form composition of the Schroder House designed by Gerrit Rietveld. So the layer of similarity is important for associating ideas. Each layer contains different data type, user can design the similarity function according to different data type, the mapping Table as shown in Table 4.1.(i) Category-based
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Feature Similarity (CBFS) is for attribute comparison, (ii) Coverage Similarity (CS) is for query topology comparison, (iii) Sequence Similarity (SS) is for spatial sequence comparison, (iv) Complete Case Similarity (CCS) is for whole case comparison.
Table 4.1 The mapping Table of data type and similarity function
(1) Category-based Feature Similarity (CBFS) (Jaccard similarity coefficient) Definition 4.1 Category-based Feature Similarity (CBFS)
FVA is the Feature Value of Feature A in one case and FVA’ is the Feature Value of Feature A in the compared case.
Example 4.1
A A'
A A'
|FV FV | CBFS=
|FV FV | I U
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(2) Coverage Similarity (CS)
The case is similar to the composition of the coverage and sequence similarity. Coverage similar to a similar number of genotypes refers to the ideal model case between genotype and genotypes compared to the case library cases, as well as the type of means of sequence similarity between the ideal task for the genotype and genotype compared to the case database case. In order to calculate the topological similarity of the cases, we must work to find a similar comparison of the expectations of the cases, genotype and type of the first, and take them as the same situation, the calculation of similar genotypes. The physical meaning of the scope of coverage is comparing to a number of similar tasks on the total number of tasks required for the tasks or genotype flow (depending on the different circumstances), which is defined as follows:
Definition 4.2 Coverage Similarity
1.CS = NCS * RCS is the coverage similarity between the query desired genotype pattern and the compared genotype, where
NCS is the coverage similarity of node (room).
RCS is the coverage similarity of relation (connection).
2.
,where
NCMatch() is the node (room) coverage, as shown in Algorithm 4.1.
TNNQ is the total number of nodes in the queried space.
3.
, where
RCMatch() is the relation (connection) coverage, as shown in Algorithm.
TNRQ is the total number of relations in the queried relation.
NCMatch(Px)
NCS= TNNQ
RCMatch(Px)
RCS= TNRQ
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Example 4.2 (a)
Example 4.2 (b) Algorithm 4.1 NCmatch Input: Px
Output: Match
Definition of Symbols:
CTi: The Compared spatial sequence i in the compared case
Step 1. Compare Px with the spatial sequences in the case , if Max( Similarity (Px,CTi) ) > threshold, then set (Px, CTm) a case pair and set Match = 1, else Match = 0
Step 2. Return Match
Algorithm 4.2 RCmatch Input: Px
Output: Match
Definition of Symbols:
CTi: The Compared spatial sequence i in the compared case
Step 1. Compare Px with the spatial sequences in the case , if Max( Similarity (Px,CTi )) > threshold, then set (Px, CTm) a case pair and set Match = 1, else Match = 0
Step 2. Return Match
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(3) Sequence Similarity (SS)
For sequence similarity, the main idea is to find similar possible sequence, where the possible sequence is the combination of every two genotypes in case.
For example, there are 3 combinational pairs A->B, B->D, and A->D for task flow A->B->D. In order to calculate sequence similarity, first step is to find similar sequence pairs, which means two A->B and A'->B', A->B is in desired task flow and A'->B' is in the compared task flow, where (A, A') and ( B, B') are two similar case pairs. The sequence pair similarity is the similarity average of 2 similar cases which is showed in Example 4.3, and the overall sequence similarity for a case is to equalize each similar sequence pair among all possible sequence.
The definition is shown as follows:
Definition 4.3 Sequence Similarity
1. SS = NSS * RSS is the sequence similarity between the query desired room private level and the compared genotype, where
NSS is the sequence similarity of node (room).
RSS is the sequence similarity of relation (connection).
2.
,where NSMatch() is shown in Algorithm 4.3
TNNS is the total number of nodes in all cases.
3.
,where RSMatch() is shown in Algorithm 4.4
TNRS is the total number of relations in all cases.
NSMatch(Px)
NSS= TNNS
RSMatch(Px)
RSS= TNNS
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Sq = (ST, DT) is the possible sequence generate from the query desired flow ST ={t1, t2,.. tn} is the source genotype in genotype sequence
DT ={t1, t2,.. tn} is the destination genotype in genotype sequences
Example 4.3 (a)
Example 4.3 (b)
(4) Complete Case Similarity (CCS) Algorithm 4.3 NSmatch Input: Sq
Output: NSMatch
Step 1. Find if there is a matched sequence node in the compared case spatial sequence, if found then go to step 2, else end.
Step 2. NSMatch = ( TSSimilarity(ST) + TSSimilarity(DT) ) / 2 Step 3. Return NSMatch
Algorithm 4.4 RSmatch Input: Sq
Output: RSMatch
Step 1. Find if there is a matched sequence relation in the compared case spatial sequence, if found then go to step 2, else end.
Step 2. RSMatch = (TSSimilarity(ST)+ TSSimilarity(DT)) / 2 Step 3. Return RSMatch
1/3, 1/3
1/3, 1/6
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In complete case retrieval, a complete case similarity is calculated to retrieve an integral case, which is most similar to, desired case, in which both cases featuring table similarity and case genotype are used. For the case feature Table, it means to find out the average similarity between each feature Table. The complete case similarity is defined as below:
Figure 4.2 The hierarchical query process
(i) SIM_Layer1 (Case_q, Case_n) = ∑CBFSn(Case_q, Case_n) (ii) SIM_Layer2 (Case_q, Case_n) = ∑CBFSn(Case_q, Case_n) Algorithm 4.5 Similarity comparison process
Input: Case
Output: Case Number
Step 1. Test if similarity Layer1 of Retrieved Case < threshold.
True -> Return NULL
Step 2. Test if similarity Layer2 of Retrieved Case < threshold.
True -> Return NULL
Step 3. Test if similarity Layer3 of Retrieved Case < threshold.
True -> Return NULL False -> Return Case Number
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(iii)SIM_Layer3(Case_q,Case_n)=∑{CBFSn(Case_q, Case_n)+CSn(Case_q, Case_n) + SSn(Case_q, Case_n)}
Example 4.4
Figure 4.3 An example of similarity calculation
4.3 Query Language and Intelligent Query Generator (IQG)
Query language (QL)
Based on the concept above, we define a set of regular grammar, called the Query Language (QL), where the grammar rule of QL can be used to model the
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schematic query, the non-terminals of QL represent the query run-time status, and the terminals of QL represent the actions the examinee can perform.
Definition 4.4 Query Language
Query Language is a 5-tuple, QL= (N, ∑, P, S, γ), where
1. N is a finite set of non-terminal, which represents the run-time status of specific query.
2. ∑ is a finite set of terminals, which represents the actions that the query can perform, e.g., attribute select.
3. P is a finite set of production rules, which represents the action performed by the query and the next run-time status of specific query. A production rule needs to satisfy one of the following forms..
4. S is the starting symbol, which represents the initial run-time status.
5. γ is a finite set of action symbols, which is defined on ∑ to trigger corresponding action routine.
Table 4.2 The description of QL symbols
Type Symbol Descript
S The starting query
symbol.
Non-terminal
Q The query symbol.
AND The Boolean operation
symbol.
OR The Boolean operation
symbol.
. The location symbol.
. The location symbol.