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Design-by-analogy: A characteristic tree method for geotechnical engineering
Automation in Construction 87 (2018) 13–21
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Automation in Construction journal homepage: www.elsevier.com/locate/autcon
Design-by-analogy: A characteristic tree method for geotechnical engineering
T
⁎
ZhiJia Youa, , HouLi Fub, Jian Shia a b
College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, China School of Civil Engineering and Architecture, Linyi University, Linyi 276000, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Geotechnical engineering Design-by-analogy Meta-synthesis Characteristic tree analogy method Decision support system
Geotechnical engineers frequently use design-by-analogy methods to promote innovative design solutions, or reuse existing design schemes. However, this approach has not yet provided a means for comparing various potential project solutions quantitatively. Moreover, while geotechnical engineering has accumulated data in large quantities, the value of this historical data has not been exploited fully for the identification of useful analogies. To address these challenges, we proposed the characteristic tree analogy method and a key algorithm for calculating the similarity index between objects. On this basis, we developed a decision support system that makes comprehensive use of geotechnical engineering historical data. We applied the system successfully to the roadway support design for Liangjia coal mine. The results verified the applicability of the characteristic tree analogy method for realizing geotechnical engineering designs, making maximum use of historical data. This approach can be extended to other areas of geotechnical engineering that have large quantities historical data.
1. Introduction Geotechnical engineering studies rock mass, soil, and other aspects of the geological environment as required for civil engineering projects. The non-uniformity, non-continuity, and uncertainty of natural conditions present challenges that cannot be solved by simple analytic methods. From the perspective of system engineering, geotechnical engineering is a complex system, making the precise design by geotechnical theoretical models is difficult to realize. Often, in real-life projects, geotechnical engineers can achieve efficient reuse of design solutions by employing analogies that reveal the similarity between projects based on generalized rock mass characteristics or expert experience [1–3]. It is well known that human thinking can promote and clarify decision-making by combining imagination with abstract thinking organically. However, it has obvious limitations. For instance, analogies can be influenced easily by subjective factors or restricted by an expert's own knowledge, and the results might provide only qualitative judgements [4]. For geotechnical engineering, there are two important keys to design development using analogies: the quick retrieval of the objects in the domain to which the analogy is applied, and the effective analysis of similarities and differences. In geotechnical engineering, the integration of influential factors to make quantitative judgments about similarity remains a challenge to be solved. Various scholars have explored the
⁎
analogy methods in this field. For instance, Yang [5] proposed the “analogic index” as a semi-quantitative experience index to describe the comparability between different projects. Zhou [6] applied a fuzzy mathematical method to estimating quantitatively, or semi-quantitatively, the influence of a single influential factor on the overall evaluation of landslide control engineering. Nevertheless, the present quantitative analogy methods still face many limitations. (1) They do not take into consideration the hierarchy of the various influential factors on geotechnical engineering, and cannot reflect the incidence relation between the influential factors at different levels. (2) They are unable to adjust flexibly to the analogy patterns according to a specific objective. (3) Each calculation step involves repeated artificial judgment and intervention, which makes it difficult to realize these steps by programming. In recent years, there have been advances in research focused on the application of decision support systems in real-life projects. Accorsi [7] developed a decision support system for storage design and operations based on a top-down methodology. Scott [8] integrated the AHP–QFD method with chance constrained programming, and developed a decision support system for supplier selection and order allocation. Taormina [9] proposed a new hydrological model for input variable selection, and applied it to streamflow forecasting. Further, Wang [10] presented an auto-regressive integrated moving average model coupled with ensemble empirical mode decomposition for forecasting an annual
Corresponding author. E-mail address: [email protected] (Z. You).
https://doi.org/10.1016/j.autcon.2017.12.008 Received 16 August 2016; Received in revised form 6 December 2017; Accepted 7 December 2017 0926-5805/ © 2017 Elsevier B.V. All rights reserved.
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“elastic wave velocity” and the abstract characteristic “structural plane characteristic”.
runoff time series. Chau [11] developed a hybrid model integrating artificial neural networks and support vector regression for daily rainfall prediction. With the arrival of the era of big data, more attention is being given to the value of data resources. The practice of geotechnical engineering has accumulated a large quantity of data, but the value of this data has not been explored thoroughly. Research focused on mining this historical data is rare, even though design-by-analogy methods need data to develop appropriate and effective analogies. To overcome the shortcomings of the prior methods, in this paper we proposed a method that uses a characteristic tree model to describe the experience of experts. Based on this method, we provided a decision support system for the Liangjia coal mine roadway that made comprehensive use of the available historical data. The application of this method effectively solved two difficulties for practical engineering: the complete dependence of support design on the experience of experts, and the inability to utilize historical design data fully.
2.2. Precondition for applying characteristic tree analogy The precondition for the application of a characteristic tree analogy is that the attribute data of the object must be stored in a relational database. Moreover, the data relations should at least meet the requirements of the second normal form (2NF) of the database. 2.3. Characteristic tree model Each characteristic of the object is regarded as a node. Together, these nodes constitute a tree-shaped data structure, called a characteristic tree model. The abstract characteristics are on non-leaf nodes, while the concrete characteristics are on leaf nodes. The root node is a special abstract characteristic, representing the overall concept of the object. To evaluate the analogy criteria quantitatively, the concept of characteristic weight is introduced to indicate the degree of influence of sub-characteristics on parent characteristics. The root node weight is set as 1. If the abstract node ANode has n sub-characteristics, that are ANode(i), where i ∈[1,n], then
2. Characteristic tree analogy The characteristic tree analogy method begins by using expert knowledge and experience to break down the overall concept of an object into microscopic characteristics from the top down. Next, the method develops a contrast mapping between characteristic values through computational means, and then calculates the degree of analogy between objects quantitatively from the bottom up. Finally, the calculated results are fed back to the experts for comprehensive evaluation. In this way, the model's intelligent human-computer interaction provides an analysis of similarities and differences between objects. In essence, the characteristic tree analogy method is a form of meta-synthesis [12] composed of an expert system (made up of domain experts), knowledge representation system (with the characteristic tree as the carrier), and tool system (database and computer program).
n
∑ ANode(i). weight = 1 i=1
Different from the Analytic Hierarchy Process (AHP), the weight of each sub-characteristic in the characteristic model represents the importance of its parent characteristic rather than the root node directly. This weight representation avoids the difficulty of making a direct comparison of the importance of sub-characteristics belonging to different parent characteristics. This approach accords with the cognitive thinking mechanisms of humans about objects. For our work, we applied the precedence chart method to assign weights to the sub-characteristics. As shown in Table 1, we compared the importance of sub-characteristics in pairs according to experts' knowledge and experience. For i,j ∈[1,n], if ANode(i) is more important than ANode(j), then Wij = 1 is obtained; if ANode(i) and ANode(j) are of the same importance, then Wij = 0.5 is obtained; otherwise if ANode (j) is more important than ANode(i), then Wij = 0 is obtained. The comparison results are input into the precedence chart to obtain the priority sequence value (PSV) of ANode(i):
2.1. Basic theory and hypothesis The characteristic tree analogy method considers that every object possesses numerous attributes. The attribute subset demonstrating the similarities and differences between objects is called a characteristic. Characteristics are divided into concrete characteristics and abstract characteristics. The idea is that all objects can be represented through their various characteristics according to a certain hierarchy.
n
2.1.1. Concrete characteristics Concrete characteristics have their own characteristic values. They can be used to describe abstract concepts, but they cannot be described by other characteristics. Concrete characteristics are classified into qualitative and quantitative characteristics. The set of qualitative characteristics is a finite set. For example, the “degree of weathering of rock mass” is considered to be a qualitative characteristic, with its five different weathering degrees – non-weathered, slightly weathered, weakly weathered, fully weathered, and strongly weathered – set as its characteristic values. The characteristic value of a quantitative characteristic can be measured in terms of quantity or amount. For instance, “compressive strength”, “slope height” and “tunnel length” can have certain numeric values as their characteristic values. The differences between the characteristic values of various objects can be evaluated quantitatively using a mathematical method.
Ai =
∑ Wik k=1
The weight of ANode(i) is the ratio of its priority sequence value to the sum of priority sequence values of all sub-characteristics in the precedence chart: n
ANode(i). weight = Ai/
∑ Ak k=1
A simple characteristic tree model is shown in Fig. 1. 2.4. Analogy quantitative index: similarity index A similarity index (SI) reflects the degree of similarity between two Table 1 Precedence chart of sub-characteristics.
2.1.2. Abstract characteristics Abstract characteristics are abstract concepts without concrete characteristic values. They can be described by other abstract characteristics or by concrete characteristics that are sub-characteristics of abstract characteristics. For instance, as the abstract characteristic, “rock mass integrity” can be described by the concrete characteristic
ANode(1) ANode(2) …… ANode(n)
14
ANode(1)
ANode(2)
……
ANode(n)
W11 W21 …… Wn1
W12 W22 …… Wn2
…… …… …… ……
W1n W2n …… Wnn
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Fig. 1. Sketch map of characteristic tree model.
Root (1.00)
Abstract (0.56)
Concrete (0.33)
Concrete (0.25)
Abstract (0.75)
Concrete (0.56)
Concrete (0.33)
CharacteristicTree +Root : Characteristic +SI : float +CCI : float +DiffQueue : QueueType -InitTree() -DestoryTree() +Analogism() : float +MemberShip() : float +SaveSI()
StackNode +value : long double -InitStacknode() -DestoryStacknode()
Abstract (0.11)
Concrete (0.50)
Concrete (0.11)
Abstract (0.50)
Concrete (0.75)
Concrete (0.25)
Fig. 2. Class diagram of the data structure.
1
0..*
1..*
1
Characteristic +type : char +name : char +value : char +weight : float +threshold : float +CStack : Stack -InitNode() -DestoryNode()
Stack -*Node : StackNode -Top : StackNode -Base : StackNode -InitStack() -DestoryStack() +isEmpty() : bool +Push() +Pop() contribution of the degree of similarity of a sub-characteristic to its parent characteristic, which is equal to the sub-characteristic's weight multiplied by its similarity index:
different characteristics. The value range of an SI is from 0 to 1. As the value becomes larger, so does the degree of similarity. When the value of the SI is 1, the two characteristics are completely identical; if the value of the SI is 0, the two characteristics are totally different. To calculate the similarity, it is first necessary to introduce the characteristic contribution index (CCI). The CCI indicates the proportional
CCI = weight∗SI As for qualitative characteristic node QL, when its characteristic 15
Automation in Construction 87 (2018) 13–21
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Begin
P=Pa
Quantitative
P.type==?
Qualitative
Abstract SI=0 Pa.value==Pb.value
SI=MemberShip(Pa.value,P b.value) isEmpty(P.stack)
Y
N SI=1 *Pc=Pa.Stack.Pop; *Pd=Pb.Stack.Pop; Pa=Pc.value; Pb=Pd.value;
SI < P.threshold
N
SI=0
Y Y
DiffQueue.Inqueue(P.na me, Pa.value, Pb.value)
SI+=Analogism(Pa,Pb); DiffQueue.Inqueue(P.na me, Pa.value, Pb.value)
N
SaveSI(P.name,P.type,SI)
CCI=P.weight*SI
Return CCI
End Fig. 3. Algorithm flow chart.
values are the same, then QL. SI = QL. weight; otherwise, QL. SI = 0. Quantitative characteristic node QN uses membership functions to calculate the SI, such as the normal distribution or the Cauchy distribution. The choice of membership functions depends on the statistical analysis of the characteristic values in the historical data. SI is equal to the membership degree of the two characteristic values, taking the normal distribution membership function as an example:
Table 2 Characteristic weight calculation of engineering geological conditions.
W1 W2 W3 W4 W5 W6
W1
W2
W3
W4
W5
W6
PSV
Weight
0.5 0 0 0 0 0
1 0.5 1 0 0 0
1 0 0.5 0 0 0
1 1 1 0.5 1 1
1 1 1 0 0.5 0
1 1 1 0 1 0.5
5.5 3.5 4.5 0.5 2.5 1.5
0.31 0.19 0.25 0.03 0.14 0.08
QN. SI = exp[−(r − 1)2] In this function, r is the ratio of two quantitative characteristic 16
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3.2. Details of the algorithm for analogy analysis
Table 3 Attributes of the characteristic nodes. Node no.
Node name
Parent node
Node type
Weight
A00 A01 A02 C01 C02 C03 C04 C05 A03
Roadway characteristics Basic characteristics Roadway size Roadway shape Section area Roadway width Wall height Arch rise Engineering geological conditions Roof rock type Floor rock type Surrounding rock type Strata inclination Groundwater characteristic Depth of roadway Roadway type Application Construction method Service life Mechanical characteristics Roof rock characteristics Compressive strength of roof rock Shear strength of roof rock Floor rock characteristics Compressive strength of floor rock Shear strength of floor rock Surrounding rock characteristics Compressive strength of surrounding rock Shear strength of surrounding rock Deformation characteristics Deformation type Deformation quantity
None A00 A01 A02 A02 A02 A02 A02 A01
Root node Abstract Abstract Qualitative Quantitative Quantitative Quantitative Quantitative Abstract
1.00 0.56 0.08 0.36 0.04 0.28 0.16 0.16 0.31
A03 A03 A03 A03 A03 A03 A01 A01 A01 A01 A00 A04 A05
Qualitative Qualitative Qualitative Quantitative Qualitative Quantitative Qualitative Qualitative Qualitative Quantitative Abstract Abstract Quantitative
0.31 0.19 0.25 0.03 0.14 0.08 0.25 0.14 0.03 0.19 0.33 0.56 0.75
A05 A04 A06
Quantitative Abstract Quantitative
0.25 0.11 0.25
A06 A04
Quantitative Abstract
0.75 0.33
A07
Quantitative
0.50
A07
Quantitative
0.50
A00 A08 A08
Abstract Qualitative Quantitative
0.11 0.75 0.25
C06 C07 C08 C09 C10 C11 C12 C13 C14 C15 A04 A05 C16 C17 A06 C18 C19 A07 C20 C21 A08 C22 C23
In our approach, the characteristic tree instances of the original object and target object were initialized respectively based on the characteristic tree model. The recursive multiway tree ergodicity algorithm was adopted in the Analogism method [13], where the input parameters are the pointer variables of the two characteristic nodes, *Pa and *Pb, and the return value is the CCI. Because the weight of the root node is 1, its SI is the same as the CCI. Therefore, when the input parameters are the root nodes of the two characteristic trees to be compared, the value returned is the similarity index of the root node. In the Analogism method, *p is defined as a variable pointing to the current access node, while the pointer variables StackNode *Pc, and *Pd point to the top nodes of the two sub-characteristic stacks respectively. As shown in Fig. 3, when the algorithm starts running, it first judges the characteristic type of the current node. If the node is a quantitative characteristic, the corresponding membership function will be called to compute the SI. If the SI is less than the threshold, the characteristic name and two characteristic values are inserted into the difference characteristic queue. If the current node is a qualitative characteristic, the algorithm judges whether the two characteristic values are equal. If so, SI = 1; otherwise SI = 0, and then the corresponding characteristic name and two characteristic values are inserted into the difference characteristic queue. If the current node is an abstract node, first the SI is zeroed out, and loops are used to judge whether there are any sub-characteristics that have not been accessed. If so, the CCIs of the sub-characteristics are accumulated to calculate the SI of the parent characteristic. The algorithm then saves the SI of the current characteristic, and finally calculates and returns the CCI. 4. Application example: soft rock roadway support design The Liangjia coal mine is a typical soft rock mine whose rock mass structure is weak, loose, and fragmented. Furthermore, the rock mass mechanics are low in strength, easily weathered and expanded, and rheological. The roadway pressure is high and fast, and the surrounding rock stability is difficult to control [14–15]. In the past, the design of roadway support relied heavily on the understanding and judgment of experienced engineers regarding the geological conditions of the mine. Clearly, dependence on the availability of specific personnel can present problems. If the experienced engineers should leave the organization for any reason, their successors will find it difficult to find and utilize the same level of experience. In addition, when faced with difficulties, the newly arrived engineers may need to consult external research institutions, thereby increasing the operating costs of the enterprise. To improve the reliability of the support scheme, and make full use of prior cases of roadway support design, we collected the roadway section and support data of more than 500 roadway sections, and established the roadway support database. On this basis, we developed the Decision Support System of Roadway Support Design based on the characteristic tree analogy method. To meet the algorithm requirements mentioned in Section 3, such as the pointer variables and the dynamic allocation of memory, we adopted C++ as the development language. Microsoft Visual Studio was adopted as the development tool because it has rich graphical interface development components, and the Microsoft SQL Server was adopted as the database management system because of its compatibility with Visual Studio. We gathered a group of experts (three mining engineers, two professors of rock mechanics, and one system developer) to construct the characteristic tree model of the roadway. To unify the experts' opinions, we applied the Delphi method to the experts' discussion. The weights of sub-characteristics were calculated by the method described in Section
values, i.e., the ratio of the larger value to the smaller value. If the abstract characteristic node ANode has n sub nodes that are ANode(i), and i ∈[1,n], then the following equation is obtained: n
ANode.SI =
n
∑ ANode(i). CCI = ∑ ANode(i). weight∗ANode(i). SI i=1
i=1
In conclusion, the similarity between two objects can be described by the similarity index of the root nodes: n
Root.SI =
n
∑ Root(i). CCI = ∑ Root(i). weight∗Root(i). SI i=1
i=1
3. Key algorithm for analogy analysis 3.1. Data structure definition For this work, we adopted the object-oriented method shown in Fig. 2. The data structure was described by the class diagram of the Unified Modeling Language. The characteristic class was defined as containing characteristic attributes such as type, name, value, weight, and threshold. We used a stack to record the addresses of sub-characteristic nodes. A characteristic tree is composed of characteristic nodes. In the CharacteristicTree class, attributes such as Root, SI, and CCI were defined, as well as methods such as the Membership method, the Analogism method (which compares two characteristic nodes), and the SaveSI method (which saves the SI to the database). 17
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Fig. 4. Construction of characteristic tree model.
Fig. 5. Interface of analogical analysis.
(W6). The calculation of these six sub-characteristics' weights is shown in Table 2. The weight of the sub-characteristics of other abstract characteristics can be calculated in the same way. All the characteristic attributes
2. For instance, the six sub-characteristics of the abstract characteristic “Engineering geological condition” were “Roof rock type” (W1), “Floor rock type” (W2), “Surrounding rock type” (W3), “Strata inclination” (W4), “Ground water characteristic” (W5), and “Depth of roadway” 18
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Fig. 6. List of difference characteristics.
roadways respectively. A sample screen is shown in Fig. 6. The calculation result in Fig. 5 shows that the similarity index between roadway LJCDF(1-2) and the original roadway was 0.832, indicating a high degree of similarity between these two roadways. Therefore, the support design scheme of this roadway can be used as the reference scheme for the original roadway. As shown in Fig. 5, when the user selects the target roadway and clicks the Support Design Scheme button, the Support Design window pops up. This window locates the corresponding Support Type option automatically, and displays the support design parameters of target roadway LJCDF(1-2) (Fig. 7). When the user analyzes the support design scheme of the target roadway and clicks the Scheme Optimization button, the design parameters become editable. The user can adjust and optimize the design scheme based on the actual current situation, and then click the Generating Support Scheme button when finished. The support design scheme for the original roadway LJFXY(1-1) will be generated automatically. Fig. 8 shows the support design drawing of the roadway section based on the support design scheme. Roadway construction was carried out in accordance with the support design scheme provided by the system. After construction, the roadway retained long-term stability. Having been tested in practice, the support design scheme of roadway LJFXY(1-1) was added to the roadway support database. In this manner, the system constantly accumulates historical data regarding roadway support designs. Since the decision support system was applied, the historical data of the Liangjia mine was utilized fully, solving the problem of relying heavily on experts for roadway support design. In addition, the reliability and efficiency of the roadway support design were improved, while design costs were reduced.
(nodes) of the characteristic tree model are shown in Table 3. The characteristic tree model and the information about the characteristic nodes can be established and maintained in the characteristic tree module. The structure of the characteristic tree model for roadway characteristics is shown in Fig. 4. Each concrete characteristic node is bound to a corresponding attribute field name in the database. Therefore, when selecting a roadway section, the system can read the database and form a characteristic tree instance automatically. For this research, one section of the Liangjia coal mine roadway was taken as an example (Number LJXFY(1-1)). Its basic parameters were input into the system through the Basic Data module. This roadway, located in a coal seam with a depth of 380 m and roof thickness of 13.35 m, and containing clay rock and siltstone, was characterized by expansibility and poor self-stability. The width of the roadway was 3.2 m and the wall height was 2.0 m. When a user opens the analogy analysis window of the Decision Support System of Roadway Support Design, as shown in Fig. 5, the first step is to click the OPT button to select the Original Roadway to be compared. Then the system reads the characteristic data of this roadway from the database, and generates a characteristic tree instance automatically. Roadway Type, Roadway Application, and other key characteristics are used as filters for searching for the target roadway. If the user clicks the Retrieval of Similar Roadways button, the system will search for target roadways that fit the filter conditions, and then initialize characteristic tree model instances. Analogical mapping is then carried out between these characteristic tree instances and the original roadway tree one by one to calculate the similarity indexes, which are ranked from highest to lowest. In general, the interface list displays the resulting information about target roadways with similarity indexes ranked in the top five. When the user selects a target roadway (for example, LJE3U(2-2)), and chooses the List of Difference Characteristics option (Fig. 5), the list of difference characteristics will be displayed in the interface window, along with the value of each characteristic for the original and target
5. Discussion Compared with past methods mentioned in the Introduction section of this paper, the characteristic tree analogy method reflects the 19
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Fig. 7. Interface of design scheme query.
6. Conclusion
hierarchical relationships between different factors. In addition, the characteristic tree model can be adjusted flexibly according to a specific target, and is easy to program. The proposed decision support system was supported by characteristic tree analogy method that made comprehensive use of historical data. The full use of historical data makes the system important for new engineering designs. Compared with previous applications of design-by-analogy in engineering, the characteristic tree analogy method overcomes drawbacks such as susceptibility to subjective factors and inability to provide quantitative analysis. It provides an organic combination of the complementary advantages of computer and human thinking. In this sense, this method can be considered as a computational simulation of human analogical thinking under the current technical conditions. The reliability of the characteristic tree analogy method depends on the structure of the characteristic tree model and the assignment of the characteristic weights. It should adopt different decision-making methods in accordance with specific conditions to resolve conflicting opinions among experts, for example, by applying the expert discussion method or the Delphi method, or a combination of both. The threshold of a characteristic is set according to expert experience. (In the case of Liangjia coal mine, the threshold was set to 0.35.) When the SI between characteristics is lower than the threshold, the algorithm considers that a difference exists between them. The method used for determining the objective threshold needs further study.
While geotechnical engineering has accumulated data in large quantities, the value of this historical data has not been exploited fully for the identification of useful analogies. To make better use of available data, this paper proposed a characteristic tree analogy model to describe the experience of experts. First, our proposed approach breaks down the overall concept of the object into characteristics from the top down, and then calculates the similarity index of two objects quantitatively from the bottom up by creating a mapping between characteristic values. The combination of expert experience, knowledge systems, and computer technology was achieved during this process. On this basis, we developed the Decision Support System of Roadway Support Design for the Liangjia coal mine, based on the characteristic tree analogy method. The results verified the applicability and reliability of the characteristic tree analogy method. This method can be extended to other areas of geotechnical engineering that also have large quantities of valuable historical data, such as the support design of foundation ditches and slopes. A limitation of this work is that it requires all the characteristic values of the objects in the database be complete. Further study is needed to determine the best way to calculate the similarity index when a characteristic value is empty. A solution might be that a characteristic with an empty value would not be mapped, and the weights of its brother characteristics would be recalculated to ensure that their sum is still 1. More research on the characteristic tree analogy method should be
20
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Fig. 8. Drawing of roadway section support design.
conducted in the future, such as expanding the application field and optimizing the algorithm for use in a big data environment. [7]
Acknowledgments [8]
This research was sponsored by the National Natural Science Foundation of China (Grant no. 51274131). The authors are grateful for their support, and also wish to express their appreciation to the reviewers who helped shape this paper.
[9]
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Automation in Construction journal homepage: www.elsevier.com/locate/autcon
Design-by-analogy: A characteristic tree method for geotechnical engineering
T
⁎
ZhiJia Youa, , HouLi Fub, Jian Shia a b
College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, China School of Civil Engineering and Architecture, Linyi University, Linyi 276000, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Geotechnical engineering Design-by-analogy Meta-synthesis Characteristic tree analogy method Decision support system
Geotechnical engineers frequently use design-by-analogy methods to promote innovative design solutions, or reuse existing design schemes. However, this approach has not yet provided a means for comparing various potential project solutions quantitatively. Moreover, while geotechnical engineering has accumulated data in large quantities, the value of this historical data has not been exploited fully for the identification of useful analogies. To address these challenges, we proposed the characteristic tree analogy method and a key algorithm for calculating the similarity index between objects. On this basis, we developed a decision support system that makes comprehensive use of geotechnical engineering historical data. We applied the system successfully to the roadway support design for Liangjia coal mine. The results verified the applicability of the characteristic tree analogy method for realizing geotechnical engineering designs, making maximum use of historical data. This approach can be extended to other areas of geotechnical engineering that have large quantities historical data.
1. Introduction Geotechnical engineering studies rock mass, soil, and other aspects of the geological environment as required for civil engineering projects. The non-uniformity, non-continuity, and uncertainty of natural conditions present challenges that cannot be solved by simple analytic methods. From the perspective of system engineering, geotechnical engineering is a complex system, making the precise design by geotechnical theoretical models is difficult to realize. Often, in real-life projects, geotechnical engineers can achieve efficient reuse of design solutions by employing analogies that reveal the similarity between projects based on generalized rock mass characteristics or expert experience [1–3]. It is well known that human thinking can promote and clarify decision-making by combining imagination with abstract thinking organically. However, it has obvious limitations. For instance, analogies can be influenced easily by subjective factors or restricted by an expert's own knowledge, and the results might provide only qualitative judgements [4]. For geotechnical engineering, there are two important keys to design development using analogies: the quick retrieval of the objects in the domain to which the analogy is applied, and the effective analysis of similarities and differences. In geotechnical engineering, the integration of influential factors to make quantitative judgments about similarity remains a challenge to be solved. Various scholars have explored the
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analogy methods in this field. For instance, Yang [5] proposed the “analogic index” as a semi-quantitative experience index to describe the comparability between different projects. Zhou [6] applied a fuzzy mathematical method to estimating quantitatively, or semi-quantitatively, the influence of a single influential factor on the overall evaluation of landslide control engineering. Nevertheless, the present quantitative analogy methods still face many limitations. (1) They do not take into consideration the hierarchy of the various influential factors on geotechnical engineering, and cannot reflect the incidence relation between the influential factors at different levels. (2) They are unable to adjust flexibly to the analogy patterns according to a specific objective. (3) Each calculation step involves repeated artificial judgment and intervention, which makes it difficult to realize these steps by programming. In recent years, there have been advances in research focused on the application of decision support systems in real-life projects. Accorsi [7] developed a decision support system for storage design and operations based on a top-down methodology. Scott [8] integrated the AHP–QFD method with chance constrained programming, and developed a decision support system for supplier selection and order allocation. Taormina [9] proposed a new hydrological model for input variable selection, and applied it to streamflow forecasting. Further, Wang [10] presented an auto-regressive integrated moving average model coupled with ensemble empirical mode decomposition for forecasting an annual
Corresponding author. E-mail address: [email protected] (Z. You).
https://doi.org/10.1016/j.autcon.2017.12.008 Received 16 August 2016; Received in revised form 6 December 2017; Accepted 7 December 2017 0926-5805/ © 2017 Elsevier B.V. All rights reserved.
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“elastic wave velocity” and the abstract characteristic “structural plane characteristic”.
runoff time series. Chau [11] developed a hybrid model integrating artificial neural networks and support vector regression for daily rainfall prediction. With the arrival of the era of big data, more attention is being given to the value of data resources. The practice of geotechnical engineering has accumulated a large quantity of data, but the value of this data has not been explored thoroughly. Research focused on mining this historical data is rare, even though design-by-analogy methods need data to develop appropriate and effective analogies. To overcome the shortcomings of the prior methods, in this paper we proposed a method that uses a characteristic tree model to describe the experience of experts. Based on this method, we provided a decision support system for the Liangjia coal mine roadway that made comprehensive use of the available historical data. The application of this method effectively solved two difficulties for practical engineering: the complete dependence of support design on the experience of experts, and the inability to utilize historical design data fully.
2.2. Precondition for applying characteristic tree analogy The precondition for the application of a characteristic tree analogy is that the attribute data of the object must be stored in a relational database. Moreover, the data relations should at least meet the requirements of the second normal form (2NF) of the database. 2.3. Characteristic tree model Each characteristic of the object is regarded as a node. Together, these nodes constitute a tree-shaped data structure, called a characteristic tree model. The abstract characteristics are on non-leaf nodes, while the concrete characteristics are on leaf nodes. The root node is a special abstract characteristic, representing the overall concept of the object. To evaluate the analogy criteria quantitatively, the concept of characteristic weight is introduced to indicate the degree of influence of sub-characteristics on parent characteristics. The root node weight is set as 1. If the abstract node ANode has n sub-characteristics, that are ANode(i), where i ∈[1,n], then
2. Characteristic tree analogy The characteristic tree analogy method begins by using expert knowledge and experience to break down the overall concept of an object into microscopic characteristics from the top down. Next, the method develops a contrast mapping between characteristic values through computational means, and then calculates the degree of analogy between objects quantitatively from the bottom up. Finally, the calculated results are fed back to the experts for comprehensive evaluation. In this way, the model's intelligent human-computer interaction provides an analysis of similarities and differences between objects. In essence, the characteristic tree analogy method is a form of meta-synthesis [12] composed of an expert system (made up of domain experts), knowledge representation system (with the characteristic tree as the carrier), and tool system (database and computer program).
n
∑ ANode(i). weight = 1 i=1
Different from the Analytic Hierarchy Process (AHP), the weight of each sub-characteristic in the characteristic model represents the importance of its parent characteristic rather than the root node directly. This weight representation avoids the difficulty of making a direct comparison of the importance of sub-characteristics belonging to different parent characteristics. This approach accords with the cognitive thinking mechanisms of humans about objects. For our work, we applied the precedence chart method to assign weights to the sub-characteristics. As shown in Table 1, we compared the importance of sub-characteristics in pairs according to experts' knowledge and experience. For i,j ∈[1,n], if ANode(i) is more important than ANode(j), then Wij = 1 is obtained; if ANode(i) and ANode(j) are of the same importance, then Wij = 0.5 is obtained; otherwise if ANode (j) is more important than ANode(i), then Wij = 0 is obtained. The comparison results are input into the precedence chart to obtain the priority sequence value (PSV) of ANode(i):
2.1. Basic theory and hypothesis The characteristic tree analogy method considers that every object possesses numerous attributes. The attribute subset demonstrating the similarities and differences between objects is called a characteristic. Characteristics are divided into concrete characteristics and abstract characteristics. The idea is that all objects can be represented through their various characteristics according to a certain hierarchy.
n
2.1.1. Concrete characteristics Concrete characteristics have their own characteristic values. They can be used to describe abstract concepts, but they cannot be described by other characteristics. Concrete characteristics are classified into qualitative and quantitative characteristics. The set of qualitative characteristics is a finite set. For example, the “degree of weathering of rock mass” is considered to be a qualitative characteristic, with its five different weathering degrees – non-weathered, slightly weathered, weakly weathered, fully weathered, and strongly weathered – set as its characteristic values. The characteristic value of a quantitative characteristic can be measured in terms of quantity or amount. For instance, “compressive strength”, “slope height” and “tunnel length” can have certain numeric values as their characteristic values. The differences between the characteristic values of various objects can be evaluated quantitatively using a mathematical method.
Ai =
∑ Wik k=1
The weight of ANode(i) is the ratio of its priority sequence value to the sum of priority sequence values of all sub-characteristics in the precedence chart: n
ANode(i). weight = Ai/
∑ Ak k=1
A simple characteristic tree model is shown in Fig. 1. 2.4. Analogy quantitative index: similarity index A similarity index (SI) reflects the degree of similarity between two Table 1 Precedence chart of sub-characteristics.
2.1.2. Abstract characteristics Abstract characteristics are abstract concepts without concrete characteristic values. They can be described by other abstract characteristics or by concrete characteristics that are sub-characteristics of abstract characteristics. For instance, as the abstract characteristic, “rock mass integrity” can be described by the concrete characteristic
ANode(1) ANode(2) …… ANode(n)
14
ANode(1)
ANode(2)
……
ANode(n)
W11 W21 …… Wn1
W12 W22 …… Wn2
…… …… …… ……
W1n W2n …… Wnn
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Fig. 1. Sketch map of characteristic tree model.
Root (1.00)
Abstract (0.56)
Concrete (0.33)
Concrete (0.25)
Abstract (0.75)
Concrete (0.56)
Concrete (0.33)
CharacteristicTree +Root : Characteristic +SI : float +CCI : float +DiffQueue : QueueType -InitTree() -DestoryTree() +Analogism() : float +MemberShip() : float +SaveSI()
StackNode +value : long double -InitStacknode() -DestoryStacknode()
Abstract (0.11)
Concrete (0.50)
Concrete (0.11)
Abstract (0.50)
Concrete (0.75)
Concrete (0.25)
Fig. 2. Class diagram of the data structure.
1
0..*
1..*
1
Characteristic +type : char +name : char +value : char +weight : float +threshold : float +CStack : Stack -InitNode() -DestoryNode()
Stack -*Node : StackNode -Top : StackNode -Base : StackNode -InitStack() -DestoryStack() +isEmpty() : bool +Push() +Pop() contribution of the degree of similarity of a sub-characteristic to its parent characteristic, which is equal to the sub-characteristic's weight multiplied by its similarity index:
different characteristics. The value range of an SI is from 0 to 1. As the value becomes larger, so does the degree of similarity. When the value of the SI is 1, the two characteristics are completely identical; if the value of the SI is 0, the two characteristics are totally different. To calculate the similarity, it is first necessary to introduce the characteristic contribution index (CCI). The CCI indicates the proportional
CCI = weight∗SI As for qualitative characteristic node QL, when its characteristic 15
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Begin
P=Pa
Quantitative
P.type==?
Qualitative
Abstract SI=0 Pa.value==Pb.value
SI=MemberShip(Pa.value,P b.value) isEmpty(P.stack)
Y
N SI=1 *Pc=Pa.Stack.Pop; *Pd=Pb.Stack.Pop; Pa=Pc.value; Pb=Pd.value;
SI < P.threshold
N
SI=0
Y Y
DiffQueue.Inqueue(P.na me, Pa.value, Pb.value)
SI+=Analogism(Pa,Pb); DiffQueue.Inqueue(P.na me, Pa.value, Pb.value)
N
SaveSI(P.name,P.type,SI)
CCI=P.weight*SI
Return CCI
End Fig. 3. Algorithm flow chart.
values are the same, then QL. SI = QL. weight; otherwise, QL. SI = 0. Quantitative characteristic node QN uses membership functions to calculate the SI, such as the normal distribution or the Cauchy distribution. The choice of membership functions depends on the statistical analysis of the characteristic values in the historical data. SI is equal to the membership degree of the two characteristic values, taking the normal distribution membership function as an example:
Table 2 Characteristic weight calculation of engineering geological conditions.
W1 W2 W3 W4 W5 W6
W1
W2
W3
W4
W5
W6
PSV
Weight
0.5 0 0 0 0 0
1 0.5 1 0 0 0
1 0 0.5 0 0 0
1 1 1 0.5 1 1
1 1 1 0 0.5 0
1 1 1 0 1 0.5
5.5 3.5 4.5 0.5 2.5 1.5
0.31 0.19 0.25 0.03 0.14 0.08
QN. SI = exp[−(r − 1)2] In this function, r is the ratio of two quantitative characteristic 16
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3.2. Details of the algorithm for analogy analysis
Table 3 Attributes of the characteristic nodes. Node no.
Node name
Parent node
Node type
Weight
A00 A01 A02 C01 C02 C03 C04 C05 A03
Roadway characteristics Basic characteristics Roadway size Roadway shape Section area Roadway width Wall height Arch rise Engineering geological conditions Roof rock type Floor rock type Surrounding rock type Strata inclination Groundwater characteristic Depth of roadway Roadway type Application Construction method Service life Mechanical characteristics Roof rock characteristics Compressive strength of roof rock Shear strength of roof rock Floor rock characteristics Compressive strength of floor rock Shear strength of floor rock Surrounding rock characteristics Compressive strength of surrounding rock Shear strength of surrounding rock Deformation characteristics Deformation type Deformation quantity
None A00 A01 A02 A02 A02 A02 A02 A01
Root node Abstract Abstract Qualitative Quantitative Quantitative Quantitative Quantitative Abstract
1.00 0.56 0.08 0.36 0.04 0.28 0.16 0.16 0.31
A03 A03 A03 A03 A03 A03 A01 A01 A01 A01 A00 A04 A05
Qualitative Qualitative Qualitative Quantitative Qualitative Quantitative Qualitative Qualitative Qualitative Quantitative Abstract Abstract Quantitative
0.31 0.19 0.25 0.03 0.14 0.08 0.25 0.14 0.03 0.19 0.33 0.56 0.75
A05 A04 A06
Quantitative Abstract Quantitative
0.25 0.11 0.25
A06 A04
Quantitative Abstract
0.75 0.33
A07
Quantitative
0.50
A07
Quantitative
0.50
A00 A08 A08
Abstract Qualitative Quantitative
0.11 0.75 0.25
C06 C07 C08 C09 C10 C11 C12 C13 C14 C15 A04 A05 C16 C17 A06 C18 C19 A07 C20 C21 A08 C22 C23
In our approach, the characteristic tree instances of the original object and target object were initialized respectively based on the characteristic tree model. The recursive multiway tree ergodicity algorithm was adopted in the Analogism method [13], where the input parameters are the pointer variables of the two characteristic nodes, *Pa and *Pb, and the return value is the CCI. Because the weight of the root node is 1, its SI is the same as the CCI. Therefore, when the input parameters are the root nodes of the two characteristic trees to be compared, the value returned is the similarity index of the root node. In the Analogism method, *p is defined as a variable pointing to the current access node, while the pointer variables StackNode *Pc, and *Pd point to the top nodes of the two sub-characteristic stacks respectively. As shown in Fig. 3, when the algorithm starts running, it first judges the characteristic type of the current node. If the node is a quantitative characteristic, the corresponding membership function will be called to compute the SI. If the SI is less than the threshold, the characteristic name and two characteristic values are inserted into the difference characteristic queue. If the current node is a qualitative characteristic, the algorithm judges whether the two characteristic values are equal. If so, SI = 1; otherwise SI = 0, and then the corresponding characteristic name and two characteristic values are inserted into the difference characteristic queue. If the current node is an abstract node, first the SI is zeroed out, and loops are used to judge whether there are any sub-characteristics that have not been accessed. If so, the CCIs of the sub-characteristics are accumulated to calculate the SI of the parent characteristic. The algorithm then saves the SI of the current characteristic, and finally calculates and returns the CCI. 4. Application example: soft rock roadway support design The Liangjia coal mine is a typical soft rock mine whose rock mass structure is weak, loose, and fragmented. Furthermore, the rock mass mechanics are low in strength, easily weathered and expanded, and rheological. The roadway pressure is high and fast, and the surrounding rock stability is difficult to control [14–15]. In the past, the design of roadway support relied heavily on the understanding and judgment of experienced engineers regarding the geological conditions of the mine. Clearly, dependence on the availability of specific personnel can present problems. If the experienced engineers should leave the organization for any reason, their successors will find it difficult to find and utilize the same level of experience. In addition, when faced with difficulties, the newly arrived engineers may need to consult external research institutions, thereby increasing the operating costs of the enterprise. To improve the reliability of the support scheme, and make full use of prior cases of roadway support design, we collected the roadway section and support data of more than 500 roadway sections, and established the roadway support database. On this basis, we developed the Decision Support System of Roadway Support Design based on the characteristic tree analogy method. To meet the algorithm requirements mentioned in Section 3, such as the pointer variables and the dynamic allocation of memory, we adopted C++ as the development language. Microsoft Visual Studio was adopted as the development tool because it has rich graphical interface development components, and the Microsoft SQL Server was adopted as the database management system because of its compatibility with Visual Studio. We gathered a group of experts (three mining engineers, two professors of rock mechanics, and one system developer) to construct the characteristic tree model of the roadway. To unify the experts' opinions, we applied the Delphi method to the experts' discussion. The weights of sub-characteristics were calculated by the method described in Section
values, i.e., the ratio of the larger value to the smaller value. If the abstract characteristic node ANode has n sub nodes that are ANode(i), and i ∈[1,n], then the following equation is obtained: n
ANode.SI =
n
∑ ANode(i). CCI = ∑ ANode(i). weight∗ANode(i). SI i=1
i=1
In conclusion, the similarity between two objects can be described by the similarity index of the root nodes: n
Root.SI =
n
∑ Root(i). CCI = ∑ Root(i). weight∗Root(i). SI i=1
i=1
3. Key algorithm for analogy analysis 3.1. Data structure definition For this work, we adopted the object-oriented method shown in Fig. 2. The data structure was described by the class diagram of the Unified Modeling Language. The characteristic class was defined as containing characteristic attributes such as type, name, value, weight, and threshold. We used a stack to record the addresses of sub-characteristic nodes. A characteristic tree is composed of characteristic nodes. In the CharacteristicTree class, attributes such as Root, SI, and CCI were defined, as well as methods such as the Membership method, the Analogism method (which compares two characteristic nodes), and the SaveSI method (which saves the SI to the database). 17
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Fig. 4. Construction of characteristic tree model.
Fig. 5. Interface of analogical analysis.
(W6). The calculation of these six sub-characteristics' weights is shown in Table 2. The weight of the sub-characteristics of other abstract characteristics can be calculated in the same way. All the characteristic attributes
2. For instance, the six sub-characteristics of the abstract characteristic “Engineering geological condition” were “Roof rock type” (W1), “Floor rock type” (W2), “Surrounding rock type” (W3), “Strata inclination” (W4), “Ground water characteristic” (W5), and “Depth of roadway” 18
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Fig. 6. List of difference characteristics.
roadways respectively. A sample screen is shown in Fig. 6. The calculation result in Fig. 5 shows that the similarity index between roadway LJCDF(1-2) and the original roadway was 0.832, indicating a high degree of similarity between these two roadways. Therefore, the support design scheme of this roadway can be used as the reference scheme for the original roadway. As shown in Fig. 5, when the user selects the target roadway and clicks the Support Design Scheme button, the Support Design window pops up. This window locates the corresponding Support Type option automatically, and displays the support design parameters of target roadway LJCDF(1-2) (Fig. 7). When the user analyzes the support design scheme of the target roadway and clicks the Scheme Optimization button, the design parameters become editable. The user can adjust and optimize the design scheme based on the actual current situation, and then click the Generating Support Scheme button when finished. The support design scheme for the original roadway LJFXY(1-1) will be generated automatically. Fig. 8 shows the support design drawing of the roadway section based on the support design scheme. Roadway construction was carried out in accordance with the support design scheme provided by the system. After construction, the roadway retained long-term stability. Having been tested in practice, the support design scheme of roadway LJFXY(1-1) was added to the roadway support database. In this manner, the system constantly accumulates historical data regarding roadway support designs. Since the decision support system was applied, the historical data of the Liangjia mine was utilized fully, solving the problem of relying heavily on experts for roadway support design. In addition, the reliability and efficiency of the roadway support design were improved, while design costs were reduced.
(nodes) of the characteristic tree model are shown in Table 3. The characteristic tree model and the information about the characteristic nodes can be established and maintained in the characteristic tree module. The structure of the characteristic tree model for roadway characteristics is shown in Fig. 4. Each concrete characteristic node is bound to a corresponding attribute field name in the database. Therefore, when selecting a roadway section, the system can read the database and form a characteristic tree instance automatically. For this research, one section of the Liangjia coal mine roadway was taken as an example (Number LJXFY(1-1)). Its basic parameters were input into the system through the Basic Data module. This roadway, located in a coal seam with a depth of 380 m and roof thickness of 13.35 m, and containing clay rock and siltstone, was characterized by expansibility and poor self-stability. The width of the roadway was 3.2 m and the wall height was 2.0 m. When a user opens the analogy analysis window of the Decision Support System of Roadway Support Design, as shown in Fig. 5, the first step is to click the OPT button to select the Original Roadway to be compared. Then the system reads the characteristic data of this roadway from the database, and generates a characteristic tree instance automatically. Roadway Type, Roadway Application, and other key characteristics are used as filters for searching for the target roadway. If the user clicks the Retrieval of Similar Roadways button, the system will search for target roadways that fit the filter conditions, and then initialize characteristic tree model instances. Analogical mapping is then carried out between these characteristic tree instances and the original roadway tree one by one to calculate the similarity indexes, which are ranked from highest to lowest. In general, the interface list displays the resulting information about target roadways with similarity indexes ranked in the top five. When the user selects a target roadway (for example, LJE3U(2-2)), and chooses the List of Difference Characteristics option (Fig. 5), the list of difference characteristics will be displayed in the interface window, along with the value of each characteristic for the original and target
5. Discussion Compared with past methods mentioned in the Introduction section of this paper, the characteristic tree analogy method reflects the 19
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Fig. 7. Interface of design scheme query.
6. Conclusion
hierarchical relationships between different factors. In addition, the characteristic tree model can be adjusted flexibly according to a specific target, and is easy to program. The proposed decision support system was supported by characteristic tree analogy method that made comprehensive use of historical data. The full use of historical data makes the system important for new engineering designs. Compared with previous applications of design-by-analogy in engineering, the characteristic tree analogy method overcomes drawbacks such as susceptibility to subjective factors and inability to provide quantitative analysis. It provides an organic combination of the complementary advantages of computer and human thinking. In this sense, this method can be considered as a computational simulation of human analogical thinking under the current technical conditions. The reliability of the characteristic tree analogy method depends on the structure of the characteristic tree model and the assignment of the characteristic weights. It should adopt different decision-making methods in accordance with specific conditions to resolve conflicting opinions among experts, for example, by applying the expert discussion method or the Delphi method, or a combination of both. The threshold of a characteristic is set according to expert experience. (In the case of Liangjia coal mine, the threshold was set to 0.35.) When the SI between characteristics is lower than the threshold, the algorithm considers that a difference exists between them. The method used for determining the objective threshold needs further study.
While geotechnical engineering has accumulated data in large quantities, the value of this historical data has not been exploited fully for the identification of useful analogies. To make better use of available data, this paper proposed a characteristic tree analogy model to describe the experience of experts. First, our proposed approach breaks down the overall concept of the object into characteristics from the top down, and then calculates the similarity index of two objects quantitatively from the bottom up by creating a mapping between characteristic values. The combination of expert experience, knowledge systems, and computer technology was achieved during this process. On this basis, we developed the Decision Support System of Roadway Support Design for the Liangjia coal mine, based on the characteristic tree analogy method. The results verified the applicability and reliability of the characteristic tree analogy method. This method can be extended to other areas of geotechnical engineering that also have large quantities of valuable historical data, such as the support design of foundation ditches and slopes. A limitation of this work is that it requires all the characteristic values of the objects in the database be complete. Further study is needed to determine the best way to calculate the similarity index when a characteristic value is empty. A solution might be that a characteristic with an empty value would not be mapped, and the weights of its brother characteristics would be recalculated to ensure that their sum is still 1. More research on the characteristic tree analogy method should be
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Fig. 8. Drawing of roadway section support design.
conducted in the future, such as expanding the application field and optimizing the algorithm for use in a big data environment. [7]
Acknowledgments [8]
This research was sponsored by the National Natural Science Foundation of China (Grant no. 51274131). The authors are grateful for their support, and also wish to express their appreciation to the reviewers who helped shape this paper.
[9]
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