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Expert Systems with Applications 37 (2010) 7364–7372
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An expert system using rough sets theory and self-organizing maps to design space exploration of complex products Xue-Zheng Chu a, Liang Gao a,*, Hao-Bo Qiu a, Wei-Dong Li b, Xin-Yu Shao a a b
The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, 1037, Luoyu Road, Wuhan, Hubei 430074, PR China Department of Engineering and Manufacturing Management, Faculty of Engineering and Computing, Coventry University Priory Street, Coventry CV1 5FB, UK
a r t i c l e
i n f o
Keywords: Mapping Performance space Design space Rough Sets Theory (RST) Self-organizing maps
a b s t r a c t In complex product design, product performance driving design is a new and innovative research in the engineering field. For realizing the product performance driving design, an elaborated expert system, Expert Systems for Assisting Mapping from Performance Space to Design Space (ESMPD) is proposed, which have two main modules for mapping from product performance space to interesting design space by two layers mapping method. In Rough Sets Theory Analysis Module, Rough Sets Theory (RST) is used to calculate configuration rules in incomplete configuration information system to assist product designers in mapping performance space to configuration space. In self-organizing maps Analysis Module, SOM is employed to analyze design variables and objective function based on preliminary optimization, to mapping from the fixed configuration space to smaller interesting regions in design space. The contribution of this research is utilizing the product design knowledge to guide engineer to partition and reduce the design space, which can save product design time and promote the design efficiency. Finally, a new bulk carrier design is taken as a case study to prove the validity and necessity of this expert system. The detailed analysis testifies ESMPD can effectively facilitate rapid and intelligent design, and reduce the cost of complex product design. Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction In practical engineering field, complex products/systems such as automobiles, aircrafts and ships are usually quite difficult to be configured and designed, because a large amount of multidisciplinary knowledge and expertise must be mastered by designers, and huge design space must be exploited entirely to get appropriate design solutions. During the two decades, many methodologies and methods have been developed and innovated in complex product design. Multidisciplinary design optimization (MDO) is an effective approach to design and optimize complex products or systems with coupled design functions and variables in a large design space from different disciplines (Haftka & Watson, 2005; Weck et al., 2007), Pareto Frontier is utilized for solving multiobjective optimization problems in MDO (Baykasoglu, Oztas, & Ozbay, 2009; Kim & Weck, 2006), and approximation models are employed in complex product design to reduce expensive computation of the extremely complicated design problems (Kleijnen, 2007; Li, Li, & Azarm, 2008; Wang & Shan, 2007). In substance, these methodologies belong to optimization processes in which
* Corresponding author. Tel.: +86 27 87559419; fax: +86 27 87543074. E-mail address:
[email protected] (L. Gao).
mathematical methods are used to search the best result of object function within a model. However, traditional design optimization processes are usually blind to engineers, and optimization results are only given to engineers directly. In addition, ordinarily, these results are unacceptable, for the limitation of the engineering practice. Thus, designers prefer to know the whole optimization process in detail. In other words, design optimization is urgently needed to be transparent and adjustable, in which expert experience is extracted to achieve the goal of intelligent design. Furthermore, in traditional optimization, a sampled point is randomly selected to start searching process, and then performance of this solution is evaluated (Shan & Wang, 2004). It starts from design space (design variables and their values) to performance space of complex products. We call it ‘‘forward design”. With this ‘‘forward design”, engineers will face a problem, how to use the successful constructed products’ data and design experience? The design knowledge reused maybe hard to be pushed forward under the random sample situation. Generally, products’ performance is vital for product companies, as a result, a method, which maps from performance space to design space and helps engineers to focus on smaller interesting design regions, absorbs many researchers’ attention. It will save much development time and cost. Consequently, designers urgently expect that an expert
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system that can help engineers to map from performance space (evaluation of the products’ performance) to design space (design variables and their values) is researched, in which with the past design knowledge, engineers can focus on interesting regions rapidly in the whole design space at the beginning of product optimization, it reduces the searching scope of design space, largely. In this paper, we named it ‘‘backward design”. As discussed above, an expert system that aids mapping from performance space to design space directly, handles and manages uncertainties, and helps designers to make design decisions in reducing design space, is imperative. Thus, in product design and optimization field, this research is going to study an effective expert system to help designers to exploit the global design space for presenting a relative transparent and smaller design space to accomplish intelligent product design. A promising expert system, Expert Systems for Assisting Mapping from Performance Space to Design Space (ESMPD), is designed based on Rough Sets Theory (RST) (Pawlak, 1982) and self-organizing maps (SOM) (Ritter, Martinetz, & Schulten, 1992), which belong to data mining (DM) technology, providing a relative transparent and optional optimization process for engineers and helping with mapping from performance space to design space. RST was first proposed by Pawlak (1982), which has been researched and applied in many fields (Leung, Wu, & Zhang, 2006; Pawlak & Skowron, 2007). The merit of RST is that, it only uses analyzed data to deduce the hidden rules, without correcting the missing or incomplete data of attributes in the whole information system. Shan and Wang (2004) first introduced RST to the mechanical area for mapping from performance to design space, and our research is the further and extended study. Shan and Wang provided an intuitive method to establish the mapping from the performance space to the design space directly. However, in practical engineering product design, especially in conceptual design, product configuration is usually included, and then design variables and their variation ranges should be confirmed. In accordance with this process of the conceptual product design, in this paper, the proposed expert system has two main modules for mapping from product performance space to interesting design space by two layer mapping method, at the first layer, RST is used to calculate configuration rules in incomplete configuration information system to assist product designers in mapping performance space to configuration space, and at the second layer, SOM is employed to analyze design variables and objective function based on preliminary optimization, to mapping from the fixed configuration space to smaller interesting regions in design space. In this study, product configuration space is considered a bridge to connect performance space and design space. The two layers methods for mapping from performance space to design space adapt to the product design more effectively. SOM (Kohonen, 2001) is an unsupervised neural network algorithm that projects high-dimensional data onto a two-dimensional map. The projection preserves the topology of the data so that similar data items will be mapped to nearby locations on the map. SOM has already been applied in engineering product design and optimization, most of researchers have gained much progress in multi-objective optimization (Budayan, Dikmen, & Birgonul, 2009; Parashar, Pediroda, & Poloni, 2008; Tanaka, Watanabe, Furukawa, & Tanino, 1995), where SOM is studied to analyze and make a trade-off of Pareto Sets solutions. To our knowledge, in this study, SOM is first used to accomplish the mentioned ‘‘backward design”. In this proposed expert system, two layers mapping are developed. At the first layer, RST is adopted to map from performance space to preliminary configuration space (subsystems or equipments and their variables of configurations), at the same time, the general design space (design variables and their intervals) can be fixed roughly. At the second layer, SOM is developed to
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map from preliminary configuration space to design space, analyzing the multi-dimensional design variables and their relationships that are based on the constructed kriging approximation model. To achieve the goal of focusing on interesting regions in design space, non-significant design variables are eliminated, and variable intervals are cut down. Consequently, this elaborated expert system using RST and SOM at two layers, respectively, to accomplish the ‘‘backward design”, which helps designers to reduce complex design space and save much product design time. The remainder of this paper is organized as follows. Mapping from performance space to design space and its characters are discussed in Section 2. Section 3 introduces the architecture and main functions of the innovative ESMPD. In Section 4, Configuration and Design Space Build Modules, Rough Sets Theory Analysis Module and the detailed application of RST are presented. Self-organizing maps Analysis Module and its application steps are given in Section 5. A new 50,000 DWT Handymax bulk carrier is described as a case study to prove the validity of the expert system in Section 6, and conclusions are finally made in Section 7. 2. Mapping from performance space to design space In complex product design, mapping from performance space to design space can guide engineers to quickly locate interesting regions and effectively provide relative transparent optimization process, the architecture of which is shown in Fig. 1. In design space, the horizontal ordinate is defined as: design variables, which denotes the set of multi-dimensional design variables, {X1, X2, . . . , Xn}, while the vertical ordinate is defined as: disciplines, which denotes the set of multidiscipline in product development {structure, power, . . . , fluid}. The horizontal ordinate and vertical ordinate divide design space into small grids. Each of the grids represents an interval of design variable in the given discipline. And that, the grid with shadow shows that it is the interesting regions in design space, which is located by mapping from the specific performance of the complex product. The interesting regions in the design space are usually the expected values or intervals of the design variables in the product design. In general, they lead product to have a high performance, and they have to be confirmed at the initial design stage. The black grid in design space means the missing or incomplete information. There are lots of reasons for incomplete information existing, such as, new equipment fixed in the new product, whose performance information and using experience are not stored in the product data warehouse, except for the manufacture technical parameters that are offered by the provider, consequently, some attributes of design schemes are hard to be estimated in practice. Also, some product running environment cannot be forecasted, and the expected values and intervals of design variables are hard to be estimated at the initial design stage. The two reasons result in the incomplete data in product design. Considering the missing information, it is presumed that all the past product design data and information are stored in the data warehouse, due to the physical destroyed or the peoples’ mistakes, there must be some data are lost. Accordingly, the missing or incomplete information are inevitable in product design, and they are denoted as black grids in design space in Fig. 1. In general, there are some inherent characters of mapping from performance space to design space in complex product design, which are summarized as follows: Coupled design variables: Design variables shared in two or more than two disciplines have different change trends following the different discipline specifications and requirements, respectively.
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Fig. 1. Architecture of mapping from performance space to design space.
Uncertainties: There are lots of uncertainties, such as fluctuation of product behaviour evaluation, unknown information of new technologies, ambiguous specifications in multidiscipline, and some missing or incomplete data in database. The need for more expertise: Making all of the decisions, including selection of equipments, selection of design variables in design space, evaluation of product behaviour in performance space, and so on, commonly relies on engineers’ engineering knowledge. With a view to these characters, an innovative expert system that could map from performance space to design space for assisting design engineers locating useful regions efficiently is necessary. Accordingly, an elaborated expert system using RST and SOM within two layers mapping is introduced in the following section. 3. Expert Systems for Assisting Mapping from Performance Space to Design Space (ESMPD) In accordance with the characters of mapping from performance space to design space, for achieving intelligent design and optimization, the proposed expert system, Expert Systems for Assisting Mapping from Performance Space to Design Space (ESMPD), is elaborated in this section. It includes three main functional modules and a data warehouse, i.e. Configuration and Design Space Build Module (CDSBM), Rough Sets Theory Analysis Module, self-organizing maps Analysis Module, and Case Data Warehouse. The architecture and functional modules of ESMPD is described in Fig. 2. As shown in Fig. 2, for the purpose of realizing mapping from performance space to design space to assist designers with design and optimization in interesting regions in design space, the Case Data Warehouse is necessary built to support ESMPD to reuse the past successful product data. There are three primary Databases in Case Data Warehouse, Product Performance and Consumer Investigation Database, Design Configuration Database and Design Variable Database. The main product design data in Product Performance and Consumer Investigation Database is summarized as: Performance evaluation data of the product in experiments and simulations: During the development of product design, there is lots of simulation and numerical analysis data, which is precious for the engineers as expertise in new product design.
Practical running performance data: The practical running data sometimes is different from the simulation information, due to the simulation errors and some unpredicted situation happened in running. It is of importance for engineers to refer in the future. Consumers’ comments about the product: Most consumers’ comments usually can reflect the product performance and problems, objectively. Consumers’ need and et al.: Consumers’ need is the lead of the product design, they are the motivity of new product development. The above main data builds the foundation for constructing the performance space. Design Configuration Database includes equipments combination or subsystem configurations of the past constructed products. To accomplish the product design, designers have to select many equipments and subsystems to gain the whole configuration of the product before they do the experiments and simulations. However, different combinations of equipments or different configuration ordinarily affect the performance of product. As a consequence, the configuration information of the past developed product is vital engineering knowledge for designers. The data stored in Product Performance and Consumer Investigation Database and Design Configuration Database provides the primary information for mapping performance space to configuration space. Design Variable Database stores the details about design variables, such as the types, past confirmed values, interesting intervals, and variable variation affected on the product performance, which discipline they belong to. From the Design Configuration Database and Design Variable Database engineers can select the relative disciplines and variables that are requisite data to establish the design space. Thus, the Case Data Warehouse is the base of ESMPD. With the support of Case Data Warehouse, the three modules in ESMPD reuse useful information of constructed product and experiment data to achieve mapping from performance space to design space. CDSBM uses the interface of Case Data Warehouse to collect the correlative configuration of the new product development to finish the configuration space, and choose the relative design disciplines of the new product form Design Configuration Database and Design Variable Database, and then, design variables in each discipline is selected and analyzed from Design Variable Database, after
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Fig. 2. Architecture and functional module of the Expert Systems for Assisting Mapping from Performance Space to Design Space (ESMPD).
that the design space is accomplished. Rough Sets Theory Analysis Module implements the first layer mapping, i.e. mapping from performance space to configuration space. Moreover, self-organizing maps Analysis Module realizes the second layer mapping, i.e. mapping from configuration space to design space. The main functions of this expert system are summarized as follows: complex product information management in the whole lifecycle; disciplines and design variables cross management of the complex product; definition and management of the complex product performance space and design space; calculation of the configuration rules from performance space to configuration space; construction of approximation model of the analysis problems and preliminary optimization; analysis of the relationships of design variables and filtration the relative design variables; and reduction of the design space to interesting regions. 4. Configuration and Design Space Build Module (CDSBM) and Rough Sets Theory Analysis Module 4.1. Configuration and Design Space Build Module (CDSBM) In the proposed expert system, confirm requirements of the product performances is the first step. According to the information stored in the Product Performance and Consumer Investigation Database, engineers could know the different performance of different level product and consumers’ comments. All of them are used to define complex product performance space.
After fixed performance space, ESMPD could provide information to designers for defining the corresponding design space. In the first module, Configuration and Design Space Build Module, the relative configuration will be collected in the Case Data Warehouse to organize the configuration space, then, the disciplines included in product design, would be analyzed particularly. Engineers would select which discipline should be research, and investigate the relationships among these disciplines. Where after, designers choose design variables of each discipline and define boundaries of them, even with some missing or incomplete data. With help of the data analysis, designers can define the whole configuration space and design space of the specific products in Configuration and Design Space Build Module. 4.2. Concept of RST in incomplete configuration information system Complex product design is a highly dynamic and interdependent process. In design space, every configuration of equipments and subsystems might not be perfect, but has its own advantages. Because some new technology and new equipments are adopted for improving the performance of new products, it is difficult for engineers to assess their performance. Beside the above reason, missing data is another reason for incomplete data in product configuration. As a result of the two main reasons, incomplete data is inevitable in configuration space and design space. Accordingly, RST is employed in incomplete configuration information system for mapping from performance space to configuration space. In our previous research work (Shao, Chu, Qiu, Gao, & Yan, 2009), RST is adopted in incomplete design scheme system for extracting design scheme rules, which belongs to ‘‘forward design”, whereas, in this research, RST is employed for extracting configuration rules from performance space to configuration space in incomplete configuration information system, which belongs to ‘‘backward
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design”. It is a new thought in the product performance driving design field. The definitions and explanations of RST have been discussed in detail in Pawlak (1982). In this study, a decision table consisting of configurations is denoted as ðU; A [ fdg; V; f Þ, where U is a set of product configurations; A is all attributes/variables of the configurations, (such as volume and cost); {d} is a set of decision attributes (the designers’ comments/products’ performance from performance space) of the configurations; V is the value domain of a, in which a 2 A; f is an information function f: U ? Va. Kryszkiewicz (1999) first make use of RST in incomplete information systems, by a new thought, which can successfully deduce optical certain rules and generalized rules from incomplete and imprecise data. In this paper, in the incomplete decision table of configuration space, any variable domain Va may contain special symbol ‘‘” to indicate that the value of a variable is incomplete or missing. In the incomplete decision table of configuration space, SIM(M) is defined as:
SIMðMÞ ¼ fðx; yÞ 2 U Uj8a 2 M; fa ðxÞ ¼ fa ðyÞ or f a ðxÞ ¼ or f a ðyÞ ¼ g:
ð1Þ
The set of indiscernible configurations is
SM ðxÞ ¼ fy 2 Ujðx; yÞ 2 SIMðMÞg;
ð2Þ
which denote the similarity of the every two configurations. Define the function as: oA(x) = {fd(y)|y 2 SM(x)}. oA(x) is the generalized decision in the incomplete decision table of configurations, due to the effect of the incomplete data. Let x e U and IA(x) # I{d}(x) (i.e. card(oA(x)) = 1), DU(x) is a certain x-discernibility function iff:
DU ðxÞ ¼
YX
aðx; yÞ where Y U ¼ U n Ifdg ðxÞ:
ð3Þ
y2Y
Let x e U, Dg(x) is a generalized x-discernibility function in S iff:
Dg ðxÞ ¼
Y X
aðx; yÞ; where Y g ¼ U n fy 2 UjdðyÞ 2 @ AT ðxÞg: Fig. 3. Flowchart of Rough Sets Theory Analysis Module.
y2Y g
ð4Þ With formula (3), optimal certain configuration rules can be extracted, which denote one region of performance space can be mapped directly to one region of configuration space. While, base on formula (4), optimal generalized configuration rules can be reasoned, which denote one or two regions of performance space can be mapped to one region of configuration space. It is accordance with the practical mapping requirements illustrated in Fig. 1. 4.3. Application steps and flowchart of Rough Sets Theory Analysis Module In Rough Sets Theory Analysis Module, to help designers to map from performance space to configuration space rapidly, RST is developed to extract the configuration rules in incomplete configuration information system. Fig. 3 illustrates the flowchart of Rough Sets Theory Analysis Module. Since RST cannot deal with the continuous variables, which is the disadvantage of this theory, one of the crucial problems is transforming useful continuous/ numerical variables into discrete ones, and the relationships between these two kinds of variables are stored in the Database, preparing for the use of the next step. After that, the successful cases are selected from the Data Warehouse, with the discretized variables and performance level, the incomplete decision table is accomplished. Then, RST is utilized to calculate the optimal certain configuration rules, by which useful knowledge is providing help for rapid mapping from performance space to configuration space.
And that, the optimal certain configuration rules are checked with product specifications and standards, if the answer is positive, then design engineers locate the interesting regions in configuration space with these rules. Otherwise, optimal generalized configuration rules are deduced. For one performance level, more referenced interesting regions are given by these rules, so the design specifications and standards will be easier satisfied. This iterative process will not be ended until the design specifications and standards are met. 5. Self-organizing maps Analysis Module 5.1. Brief introduction of self-organizing maps Self-organizing maps is an unsupervised learning of neural networks that has been successfully applied in data mining and visualization (Chou, Cheng, & Chang, 2007). It is a model for clustering and visualizing high-dimensional data, which groups data with similar characteristics. The purpose of visualization is to project data onto a graphical representation to provide a qualitative idea of its properties. Usually, in SOM, the multi-dimensional data is mapping to the two dimension space with hexagonal grids. Thus, it makes the multi-dimensional design variables visualization come true in complex products design. To be different from conventional geographical, SOM cannot provide any geographical
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features, coordinates, distance and so on, but it can describe closeness or distribution of the input design variables. Diagrammatic sketch of SOM is depicted in Fig. 4, n-dimensional design variables and m-objective functions vectors are input to the input layer, where n and m are positive integer, at the same time, assigned to them to each (n + m) neuron. In the output layer, n + m dimensional weight vectors V = {v1, v2, v3, . . . , vn+m} are randomly assign to neurons. In SOM algorithm, the input vectors are fully connected with neurons in the output layer. The unsupervised learning in SOM is to cluster together similar patterns while preserving the topology of input space. During this learning process, two main goals are pursuing to be achieved. The first is, output layer searches for the winning unit, which is the neuron with a closer weight vector to each input vector in the input layer. The second is, in order to be much closer to the input design variables and objective function vectors, weight vectors of the winning unit and its neighboring neurons will be updated. As a result, the n + m dimensional input vectors are projected onto a sequence of neighboring neurons in the two-dimensional hexagonal grid. Judging from changing color of the neurons in output layer, designer can compare the change trends of design variables, or the correlation between design variables and objective functions. From the above, detailed steps of application SOM in the proposed expert system is summarized as follows: Step 1: Randomly assign the weight vector V ¼ fv 1 ; v 2 ; v 3 ; . . . ; v nþm g; Step 2: Select the relative n design variables and m-objective functions as the input vectors; Step 3: Search the winning neuron that has the closest distance from input vectors; Step 4: Update the weight vectors of the winning unit and its neighboring neurons; Step 5: If the predefined iterative requirement is satisfied, stop. All the design variables and objective functions are projected onto the two-dimensional hexagonal grid. Otherwise, go to step 2. 5.2. Application steps of self-organizing maps Analysis Module In self-organizing maps Analysis Module, to map from the above fixed configuration space to design space, SOM is utilized to help designers to analyze design variables and cut down the initial design space, achieves the goals of locating interesting regions in design space directly. Considering the equipments and subsystems determined in Rough Sets Theory Analysis Module, the corresponding experiment data or practical running data are chosen from Product Performance and Consumer Investigation Database. For each past design case, design variables and their ordinary intervals are confirmed, at the same time, their running performance or experiment results are fixed as the object. After that, kriging model is built up based on these data and information. In order to know the general landscape of the interesting problem, a preliminary
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optimization is implemented on the constructed kriging model. During the preliminary optimization on kriging model, a set of data about the design variables and objective functions can be gained, and then SOM is adopted to analyze these data for getting the mutual relationships of variables and correlations between variables and objective functions. As a sensitive analysis, concerning the color change trends among them, the non-significant design variables are eliminated, also, the intervals of significant variables are reduced. Consequently, the initial design space is redefined with smaller space. As a result, in self-organizing maps Analysis Module, SOM can give a transparent design space to engineer, also help designers to analyze and reduce design space. It can save much product design time, and make optimization more easily.
6. Case study In this section, a new 50,000 DWT Handymax bulk carrier design is taken as a case study for proving the validity and necessity of the proposed expert system, Expert Systems for Assisting Mapping from Performance Space to Design Space (ESMPD). As mentioned in Section 2, Case Data Warehouse stores all aspects information of successful constructed complex products. For ship design, practical running feedback data, consumers’ comments about ships, all experiments data about ship model gained in naval tank are collected in Product Performance and Consumer Investigation Database, they are adopted to build the ship performance space. Data of the subsystems, configurations, and so on, are included in Design Configuration Database. They are used to build the ship configuration space in Configuration and Design Space Build Module. Extracting useful expertise for mapping from performance space to ship design space is significant to ship designer, because it makes product design more efficient. In conceptual ship design, main engine selection and its relative equipments arranged in pairs or groups will directly affect the whole ship’s performance, even consumers’ comments. Thus, in this paper, main engines and power systems configurations are the central researching objectives. In ESMPD, in order to design a new 50,000 DWT Handymax bulk carrier, six kinds of configurations (Shao et al., 2009) are chosen with discretized attributes (design variables) from 16 similar cases stored in the Case Data Warehouse are listed in Table 1. When some new subsystems are wanted to be equipped, because there is no information and experience of using the new systems in the past, except for the manufacture technical parameters that are offered by providers, some variables of these design schemes are hard to be estimated in practice. So, incomplete data is inevitably included in configuration decision table. The symbol ‘‘” is used to denote the incomplete values of variables. Accordingly, Rough Sets Theory Analysis Module employs RST in incomplete decision table to calculate the configuration rules from performance space to configuration space, so as to assist designers making mapping decision.
Fig. 4. Diagrammatic sketch of self-organizing maps.
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Table 1 The incomplete decision table of the six configurations. Scheme
V
M
C
R
E
Grade
oA
S1 S2 S3 S4 S5 S6
H N H H L N
L H L H L
H L H H H L
H H L
H H H H
I II II II III II
{I, II} {II} {II} {I, II} {III} {II}
In Rough Sets Theory Analysis Module, the decision table is expressed as: S = (U, A [ {d}, V, f), where U = {S1, S2, . . . , S6} is the set of these configurations of the built ships; A is the set of conditional variables that consists of V (valid utilization degree), M (maintenance cost), C (building cost), R (reliability in voyage) and E (energy consumption cost), whereas the decision variable {d} is Grade, which represents the performance grade of these configurations. The variable domains are: VV = {H (High), N (Normal), L (Low)}; VM = {H (High), L (Low)}; VC = {H (High), L (Low)}; VR = {H (High), L (Low)}; VE = {H (High), L (Low)}; VGrade = {I, II, III}, where I, II and III stand for good, normal and poor performance grade of configurations, respectively. Some of the optimal certain rules of Table 1 are concluded with formula (3) as follows: Rule 1: If maintenance cost is low or valid utilization degree is high or reliability in voyage is high and energy consumption cost is low, then Grade is I. Rule 2: If valid utilization degree is low, then Grade is III. Rule 3: If maintenance cost is high and reliability in voyage is low or energy consumption cost is low, then Grade is III. As a result of analyzing these configurations, Rule 1 illuminates that if a new ship is wanted to have a good performance, the maintenance cost should be low (1.6 104–2.2 104 dollars/week) or valid utilization degree should be high (70–80%) or reliability in voyage should be high (92–95%) and energy consumption cost should be low (1.82 105–2.1 105 dollars/day). Hence, the high level performance of configuration has already been mapped to regions of configuration space. The useful knowledge can help engineers to map from performance space to configuration space directly. On the contrary, Rules 2 and 3 explain that the poor grade of the performance can be mapped to which regions in configuration space. In practice, they should be avoided because of their unsatisfying performance. If the regions focused by the optimal certain configuration rules, do not satisfy the design specifications and standards, the optimal generalized configuration rules with a wider range of restriction are advised to be adopted to help designers. Generalized decision variables are calculated with formula (2). Some optimal generalized configuration rules in Table 1 are gotten with formula (4) as following: Rule 1: If valid utilization degree is high, then Grade is I or II. Rule 2: If maintenance cost is low, then Grade is I or II. Rule 3: If maintenance cost is high and reliability in voyage is low, then Grade is III. From the above results, some optimal generalized configuration rules can be found the same as the optimal certain ones. However, some optimal generalized configuration rules have two decision variables, so they can map two performance space to the same configuration space. In the light of Rule 1, in order to have a good or normal performance grade, ship designers should amend the design configuration to be highly validly utilized (70–80%). While,
with respect to Rule 3, it expresses that if designers want to save optimization time, regions with the configuration being hard maintained (more than 2.0 104 dollars/week) and unreliable (with 60–70% reliability) in voyage should be avoided, because of its poor performance. All the above discussions show that, in Rough Sets Theory Analysis Module, performance space is mapped to regions of configuration space effectively. It can provide another new thought for the designers to develop new complex products rapidly, according to the past successful cases’ performance. In self-organizing maps Analysis Module, to map configuration space to design space, as mentioned earlier, SOM is adopted. With the help of the optimal certain configuration rules or the optimal generalized configuration rules, considering the performance degree of ships, ship designers can quickly focus on useful regions in the configuration space. In Rough Sets Theory Analysis Module, after engineers select the main equipments and their correlative configuration, the design variables and their value intervals are confirmed, also constraints and general objective functions are determined. Accordingly, configuration space is fixed in Configuration and Design Space Build Module. The main design variables and constraints of the bulk carrier are analyzed in self-organizing maps Analysis Module, summarized in Table 2, in which the bold variables are the design requirements of ship and kept fixed, and the italic ones are constraints in preliminary optimization, while others are design variables with changing ranges. Note that this new bulk carrier is design to navigate through Panama Channel, thus beam (B) and draft (T) of the new product should be subjected to B 6 32.31 and T 6 11.71. Because ships are products to be sold, thus the profit that can be brought by ships is significant for ship design companies. To achieve the goal of maximum the profit of shipping cargo, the objective of this ship design is pursuing the minimum transportation cost, where transportation cost = annual costs/annual cargo. In the light of these list variables and constraints, the practical running data and information are selected from the Case Data
Table 2 Main variables and constraints of the new Handymax bulk carrier. Variables or constraints
Units
Value
Dead weight Service speed Ship length (o.a) (L)
T kn M
50,000 14.5 190.0
Depth (D) Beam (B) Main engine max power Oil consumption Deck thickness Fuel weight Water plane area Draft (T) Propeller efficiency Drivetrain efficiency Density of steel Voyage range Bending stress
Nm ksi (kilopounds per square inch) ksi
Shear stress Stability factor L/B L/D L/T Beam (B) (Panama Channel) Draft (T) (Panama Channel)
Min.
Max.
M m kW
16 28 8900
18 34 11000
t/day mm T m2 M
27 19.3 1000 2800 7.5 0.60 0.88 471.0
34 21.2 1400 3400 12 0.68 0.90 498.0
lb/ft3
10,000 28 28 0.0 6
M
15 19 32.31
M
11.71
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Warehouse. In self-organizing maps Analysis Module, the kriging approximation model is built up based on 75 groups of data, is illustrated in Fig. 5. Genetic Algorithm is adopted preliminarily optimize on the kriging model. As a result of this process, SOM is used to analyze the relevant design variables, the results are shown in Fig. 6. A0, A1, A2, A3, A4, A5, A6, A7 denotes beam, draft, deck
Fig. 5. Kriging model of objective function vs. fuel weight and draft.
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thickness, depth, propeller efficiency, drivetrain efficiency, fuel weight, water plane area, respectively, while Y represents objective function of the optimization (the minimum transportation cost). For analysis objective function, high values of Y are convergent in the top right corner, and for A0, high values are also convergent in the top right corner. However, the low values of Y are fastened in the down part of maps, and the low values of A0 are fastened in the central right of maps. This analysis means that, broader breadth will result to the higher cost of transportation. On the contrary, the thinnest ship body cannot increase more profit of transportation. It is because that too thin ship body cannot satisfy the structure specifications in longitudinal direction, and it reduces the stability of ship. A4 and A5 have the similar color distributions and arrangements in maps. Thus, for reducing design space, and only focus on the interesting regions, one of them regarded as non-significant variable, is eliminated. As a result, the whole ship design space will be reduced one dimension. In our study, A5, namely drivetrain efficiency is deleted in the optimization. In order to reduce design variables’ intervals, maps of variables should be compared and analyzed according to objective function. Both A2 and Y have their low value in the down part of the maps, and the preliminary optimization is to find the minimum of Y, thereby, ship designers only need to focus on the down part of A2. Consequently, the interval of deck thickness is reduced to 19.842–20.236. Comparing to the initial interval, the new interval of A2 is reduced at least 50%.
Fig. 6. Self-organizing maps of design variables and objective function.
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After analysis, the intervals of design variables are redefined as follows: A0 (30.335–31.846), A1 (8.7687–11.468), A2 (19.842–20.236), A3 (16.823–17.089), A4 (0.62530–0.66000), A5 is deleted, A6 is not changed, A7 (2936.2–3168.3). Thus, compared with the initial design space, now, design variable intervals are reduced largely, for example, the interval of A0 is (30.335–31.846) instead of the initial interval (28–34). As discussed above, in self-organizing maps Analysis Module, configuration space is mapped to smaller design space. With the smaller design space, ship designers can focus on their interesting regions in design space, which makes the succeeding strict optimization more quickly and efficiently. It is more important that the performance space is mapped to the smaller interesting regions in ship design space, by the two layers mapping method. 7. Conclusion In this paper, the elaborated expert system, Expert Systems for Assisting Mapping from Performance Space to Design Space (ESMPD) maps from performance space of complex product to the smaller interesting regions in design space, in which the two layers mapping method is implemented, i.e. mapping from performance space to configuration space, and mapping from configuration space to the regions in design space. In Rough Sets Theory Analysis Module, RST is used to deduce the configuration rules in incomplete configuration information system, to assist engineers with the first mentioned mapping. In self-organizing maps Analysis Module, SOM is utilized to analyze the preliminary optimization information to help designer to make mapping decisions from configuration space to smaller and interesting regions in design space. This proposed expert system assists designer in reusing the past useful design experience and knowledge to achieve the goal of reducing the global product design and optimization space. In product engineering design field, the contribution of this research is that, with the extracted the hided useful knowledge from past designed products, designers partitions the whole design space, and gives a relative more transparent and optimal design space to engineers. All of these can make the product development make full use of the precious past expertise, save development time and accelerate product design efficiency. In order to testify the validity and necessity of ESMPD, a new bulk carrier design is described in detailed as a case study. It is proved that the expert system can assist product designers in making the mapping decisions from performance space to interesting design space. Accordingly, ESMPD facilitates rapid and intelligent product design effectively.
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