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Abstract

Case-based reasoning has proven to be a promising methodology for obtaining new mechanical products by adapting previous cases. However, case adaptation is still a bottleneck in case-based reasoning. The key issue in case adaptation is acquiring the adaptation knowledge. To realize the automation of case adaptation for variant design, a novel case adaptation method is proposed. The method consists of two parts. In the first part, a data mining technique is introduced to acquire the adaptation rules that reflect the relationship between the changes in design requirements and design results. In the second part, the most similar case is retrieved by first using the adaptation rules to weight the design requirements. Then, suitable adaptation rules are selected and used to realize the case adaptation. To validate the proposed method, two experiments are performed. The results show that our method outperforms other methods when the design requirements and design results have both numerical and categorical attributes.

Keywords

Case adaptation case-based reasoning data mining variant design

Introduction

With the growth of global competition, manufacturers now face a more complex marketing environment and must respond to a changing market more quickly, and their product must have better performance and lower costs. As the bridge that connects the customers, manufacturers, and suppliers, design is the key to ensuring the success of a product. Variant design is a type of design that adapts previous products in the local structure or the parameters of parts to satisfy new requirements.¹ Because variant design shows significant advantages in both time and cost, it is attracting increasing attention.²

Many methods have been applied to increase the efficiency of variant design. Case-based reasoning (CBR) is one of the most widely applied techniques in this field. CBR, an artificial intelligence technique proposed by Schank,³ infers the solution to a new problem based on previous experience. A typical CBR system consists of four sequential steps that are recalled to solve a problem: retrieve the most similar case, reuse the case to attempt to solve the new problem, revise (adapt) the suggested solution as necessary, and retain the new solution.⁴ CBR has been applied in many domains, such as financial distress prediction,⁵ chemistry,⁶ medical diagnosis,⁷ environmental protection,⁸ and oceanography.⁹

In general, case adaptation is usually required to complete a new design. However, case adaptation requires extensive adaptation knowledge and takes a long time. Therefore, the automation of case adaptation can significantly increase the efficiency of variant design. Case adaptation is essential for CBR implementation, and adaptation knowledge is very important for the application of the retrieved case to the solution.¹⁰ However, since data play an important role in the process of new product development,¹¹ a large amount of design data has been collected. Therefore, mining knowledge from the design data is the key to increase the automation of case adaptation.

In this study, a data mining technique is introduced into CBR to acquire the adaptation knowledge, which is in the form of a production rule. Then, case retrieval and case adaptation are realized using the acquired adaptation knowledge.

Section “Literature review” presents a literature review. Section “Overview of the proposed method” describes the framework of the method in this study. Section “Adaptation rule acquisition” describes the method for the adaptation rule acquisition in detail. Section “Case retrieval and adaptation” describes the case retrieval and case adaptation methods in detail. Section “Case study” provides an example to illustrate the method. An experiment is shown in section “Experiments” to validate the effectiveness of the method. Section “Conclusion and future work” provides the conclusion.

Literature review

In general, a solution to a new design problem that has been retrieved cannot be used directly and must be adapted beforehand. However, case adaption is the bottleneck in CBR execution, and some studies have been performed to address the case adaptation bottleneck. Tong et al.¹² proposed an adaptation technique based on fuzzy regression for the process design of transfer molds for electronic packages. Qi et al.¹³ addressed a new case adaptation method that uses a support vector machine, which incorporates the adaptability-related knowledge provided by the retrieved cases. Hu et al.¹⁴ proposed a new case adaptation method for parametric machinery design using the weighted mean (WM). Jung et al.¹⁰ proposed a new case adaptation method based on the artificial neural network and used the method to calculate the design values of a new shadow mask. These studies can increase the automation of case adaptation to some extent, but their methods apply only to the adaptation of numerical attributes. Because a product has both numerical attributes, such as the bore diameter, and categorical attributes, such as the material, an adaptation method that supports both types of attributes is required. Vong et al.¹⁵ proposed a case-based adaptation method, which is a two-level CBR that contains a case library and an adaptation case library. However, the method applies only to a new adaptation that is completely consistent with an existing adaptation case in the library. Janthong et al.¹⁶ proposed a case adaptation method based on rule inference, but the rule acquisition remains a bottleneck in his study. Li et al.¹⁷ proposed a method of adaptation rule acquisition by manually comparing similar cases, but the method is applicable only when the case base is small and has relatively few attributes. For example, even if there are only 200 cases in the case base and each case has only 40 attributes, to extract all adaptation rules, comparisons should be performed 1,592,000 times, which cannot be handled manually. Because of the wide application of information systems, case bases usually contain many cases, and cases of mechanical design usually have many attributes, particularly for complex products.

Compared with the previous methods, our method has two main advantages that make it more applicable to variant design:

This method can handle the case adaptation with both numerical and categorical attributes.

This method can acquire adaptation rules automatically when the case base has many cases and when the cases have many attributes.

Overview of the proposed method

The method of case adaptation in this study can be divided into two main phases. In the first phase, the adaptation rules are acquired. In the second phase, the rules are used to retrieve the most similar case and adapt the retrieved case. The framework of the method is shown in Figure 1.

Figure 1.

Framework of the proposed method.

In the rule acquisition phase, the cases are first pre-processed. Then, by comparing the case pairs, the changing events are extracted to represent the difference between cases. Then, the Apriori algorithm is applied to acquire the adaptation rules that are in the form where if x (a design requirement) changes from a to b, then a design result attribute y (a design result attribute) changes from c to d. The rules are stored in the rule base.

In the variant design phase, the most similar case is first retrieved by the similarity evaluation. Then, the adaptation rules are selected and used to obtain the inference result. Finally, the inference result is transformed into the uncoded form.

Adaptation rule acquisition

In this section, the rule acquisition method based on data mining is described in detail. Data mining, a technique to discover knowledge in a database, has become a research area and has assumed increasing importance with the significant increase in the amount of data in recent years.¹⁸ The data mining technique has been widely used in many fields, including biology,¹⁹ agriculture,²⁰ medical science,²¹ and finance.²² The entire process of adaptation rule acquisition consists of two steps: data pre-processing and adaptation rule mining.

Data pre-processing

In this study, the cases are represented as attribute–value pairs, which include design requirement attribute–value pairs and design result attribute–value pairs. The requirements and results of variant design have both categorical attributes, such as the material used for the parts, and numerical attributes, such as the diameters of the holes. To realize rule mining, the raw data should be pre-processed. For the numerical attributes, equal-width binning is performed to discretize the attribute values. Equal-width binning is an unsupervised method for producing categorical values from numerical ones and involves dividing the range of observed values of a numerical attribute into K (selected by the user) equally sized bins.²³ The bin width is obtained by equation (1)

$ε = \frac{v_{\max} - v_{\min}}{K}$ (1)

where ε is the bin width of an attribute, $v_{\max}$ is the maximum of the attribute in the case base, and $v_{\min}$ is the minimum of the attribute in the case base.

Each bin of an attribute is considered a value and given a uniform code. The categorical attributes can be directly coded. The values of the design requirements are expressed as $x_{i} p_{j}$ , which implies that the value of the ith design requirement is the jth value of its range. The design result is expressed as $y_{l} a_{m} p_{n}$ , which implies that the value of the lth attribute of the mth part of a product is the nth value of its range.

The adaptation rules are obtained by analyzing the co-occurrence between the changes in the design requirements and the design results. Each change in a design requirement or design result is called a “changing event” in this study. The changing events should be extracted by comparing two cases. A changing event of a design requirement is expressed as $x_{i} c p_{j} t p_{k}$ , which indicates that the ith design requirement changes from its jth value to its kth one. In particular, $x_{i} c 0 t p_{k}$ indicates that the ith design requirement changes from nonexistence to its kth value, and $x_{i} c p_{j} t 0$ indicates that the ith design requirement changes from its jth value to nonexistence. A changing event of design result that is realized by modifying a part is expressed as $y_{l} a_{m} c p_{n} t p_{u}$ , which indicates that the mth attribute of the lth part changes from its nth value to its uth one. A changing event of a design result that is realized by reconfiguring the parts is expressed as $y_{l} c 0 t a_{m} p_{n}$ , $y_{l} c a_{m} p_{n} t 0$ , and $y_{l} c_{e} t_{f}$ . $y_{l} c 0 t a_{m} p_{n}$ indicates that the lth part changes from nonexistence to existence, and its mth attribute is its nth value; $y_{l} c a_{m} p_{n} t 0$ indicates that the lth part changes from existence to nonexistence, and the value of its mth attribute used to be its nth one; and $y_{l} c_{e} t_{f}$ indicates that the lth part of the product changes from the eth one to the fth one within its alternative part list.

Adaptation rule mining

The Apriori algorithm is used to acquire the adaptation rules in this study. The Apriori algorithm was proposed by Agrawal and colleagues^24,25 and is one of the most widely used techniques for finding association rules. The algorithm operates in two phases. In the first phase, all itemsets with minimum support (frequent itemsets) are generated. This phase uses the downward closure property of support. In other words, if an itemset of size k is a frequent itemset, then all itemsets below (k − 1) size must also be frequent itemsets. Using this property, frequent itemsets of size k are generated from the set of frequent itemsets of size (k − 1). If an itemset of size k has a subset of size (k − 1) that is not a frequent itemset, it is not a frequent itemset. The second phase of the algorithm generates rules from the set of all frequent itemsets.²⁶

A frequent itemset is an itemset with a larger support than the support threshold. The support of the itemset is obtained using equation (2)

$\sup (A, B) = \frac{N_{1}}{N_{2}}$ (2)

where $N_{1}$ is the number of itemsets that contain both items A and B. $N_{2}$ is the number of all itemsets in the set. The confidence of a rule is obtained using equation (3)

$conf (A \Rightarrow B) = \frac{\sup (A, B)}{\sup (A)}$ (3)

Definition

N − x frequent itemset is the frequent itemset that has n design requirement changing events. The steps of rule mining are as follows:

1 − x frequent itemset mining. In the first iteration, each itemset that contains one design requirement changing event and no fewer than one design result changing events is counted. Then, the itemsets in which supports are not less than the support threshold are selected to form 1 − x frequent itemsets.

N − x frequent itemset mining from (n − 1) − x frequent itemsets. An n − x candidate itemset is generated by combining an (n − 1) − x frequent itemset and a 1 − x frequent itemset. Then, the candidate itemsets whose (n − 1) − x item subsets do not belong to (n − 1) − x frequent itemsets are removed. This step is repeated until all combinations of design requirement events are traversed.

Adaptation rule generation from frequent itemsets. Transform the changing events of design requirements of a frequent itemset into the antecedent of a rule, and transform the changing events of design results in a frequent itemset into the consequence of the rule. Calculate the confidence of the rule. If the confidence is beyond the threshold, add it to the adaptation rule base.

The adaptation rules are stored in the rule base.

Case retrieval and adaptation

Variant design is realized by adapting previous design cases. Thus, the case that is most similar to the target case is retrieved first. Then, the retrieved case is adapted by the inference of the adaptation rules that were acquired in the previous section.

Case retrieval

The role of case retrieval is to find the most suitable case for the following adaptation. Case retrieval is realized by evaluating the similarity between the target case and the previous cases. The most important issue of similarity evaluation is weighting the design requirements. In this study, the weights of the design requirements are obtained by analyzing the adaptation rules. The adaptation rules express the changes in design requirements and the corresponding changes in design results. Therefore, if one change in a design requirement causes more changes in design results, the design requirement should be assigned a higher weight.

To weight the design requirements, the importance score of each design requirement is calculated first. The importance score of the ith design requirement is obtained using equation (4)

$w (x_{i}) = \frac{\sum_{j = 1}^{n} count (a_{j})}{n}$ (4)

where $w (x_{i})$ is the importance score of the ith design requirement, n is the count of rules whose antecedents have only one changing event and is the change in the ith design requirement, and $count (a_{j})$ is the count of parts in the consequence of the jth rule. The weights of the design requirements are obtained by normalizing their importance score. The weight of the ith design requirement is expressed as $W (x_{i})$ . The similarity between each corresponding design requirement of two cases is obtained using equation (5)

$s (x_{i}) = {\begin{matrix} 1 - \frac{| v_{1} - v_{2} |}{K} & if x_{i} is numerical attribute \\ 0 & \begin{matrix} if x_{i} is categorical attribute, \\ and v_{1} \neq v_{2} \end{matrix} \\ 1 & \begin{matrix} if x_{i} is categerical attribute, \\ and v 1 = v 2 \end{matrix} \end{matrix}$ (5)

where $s (x_{i})$ denotes the similarity of the ith design requirement between two cases, $v_{1}$ is the value of the ith design requirement of the target case, $v_{2}$ is the value of the ith design requirement of the previous case, and K is the number of values that the ith design requirement has.

The similarity between two cases is obtained by calculating the weighted sum of the similarity between each corresponding design requirement of two cases. The most similar case is selected for the following adaptation.

Case adaptation

The role of case adaptation is adapting the retrieved case to satisfy the new design requirements. Case adaptation is realized by the inference of adaptation rules. During the course of inference, it is possible that no single rule can realize the inference. Thus, a group of rules should be used together to complete the inference. However, there may be more than one group of rules that can realize the inference, so it is necessary to select the suitable rule group. The rule group is selected by their applicability, which is obtained using equation (6)

$A (g_{i}) = \frac{\sum_{j = 1}^{n} conf (r_{j}) \times sup (r_{j})}{n}$ (6)

where $A (g_{i})$ denotes the applicability of the ith rule group, $conf (r_{j})$ is the confidence of the jth rule in a rule group, $conf (r_{j})$ is the support of the itemset of rule $r_{j}$ , and n is the number of rules in the ith rule group.

Two rules may conflict with each other during the inference process. For example, the changes in $x_{1}$ and $x_{2}$ should occur concurrently to realize the adaptation. The value of x₁ should change from $x_{1} p_{1}$ to $x_{1} p_{2}$ . The value of $x_{2}$ should change from $x_{2} p_{2}$ to $x_{2} p_{3}$ . The value of $y_{1} a_{1}$ in the retrieved case is $y_{1} a_{1} p_{2}$ . One rule is that if the value of $x_{1}$ changes from $x_{1} p_{1}$ to $x_{1} p_{2}$ , then the value of $y_{1} a_{1}$ changes from $y_{1} a_{1} p_{2}$ to $y_{1} a_{1} p_{4}$ . The other rule is that if the value of $x_{2}$ changes from $x_{2} p_{2}$ to $x_{2} p_{3}$ , then the value of $y_{1} a_{1}$ changes from $y_{1} a_{1} p_{2}$ to $y_{1} a_{1} p_{5}$ . As a solution to the conflict, the value of $y_{1} a_{1}$ is determined by the rule with the larger confidence. The adaptation is realized through the following steps:

Extract the changing events by comparing the design requirements of the target case and the retrieved case.

Search for the single rule that exactly satisfies the changing events. If the single rule exists, the inference result is obtained directly.

If there is no single rule that satisfies the change events of the design requirements, select the rule group with the largest applicability and complete the inference.

The outputs of the rule inference are the changing events of the design result, as expressed in the coded form. To accomplish the variant design, the outputs should be translated into uncoded form. More importantly, the numerical attributes of the design result should be given exact values. The exact value of a numerical attribute is obtained in the following steps:

Select the cases that have the same encoded value with the attribute of the target case.

Calculate the similarity between the cases and the target case. The five cases with the largest similarity are selected as the valuation basis.

Calculate the weights of the cases using their similarity with the target case.

Obtain the exact value of the attribute of the target case by calculating the weighted average of the uncoded attribute values of the five cases.

Case study

An example of electromotor design is provided in this section to illustrate the proposed method of case adaptation. A model of an electromotor is shown in Figure 2. The main design requirements include rated power (RP), number of poles (NP), rated voltage (RV), rated frequency (RF), protection class (PC), cooling method (CM), mounting arrangement (MA), duty type (DT), and noise (N). The design results of variant design are the main attributes of the parts, such as the specification of the stator core (SC), specification of stator windings (SW), specification of the rotor core (RC), specification of bearings (B), specification of the fan (FA), specification of the frame (FR), and specification of the end covers (EC), as shown in Table 1.

Figure 2.

A model of electromotor.

Table 1.

Example case.

Number	Design requirements			Design result
	RF (Hz)	N (dB)	MA	SW	FA	FR	EC	B
C₁	50	56	B3	Material: QP–1/200	Blade shape: backward	Foot: existent	Flange: nonexistent	Noise free bearing: yes
C₂	50	56	B5	Material: QP–1/200	Blade shape: backward	Foot: nonexistent	Flange: existent	Noise free bearing: yes
C₃	50	56	B35	Material: QP–1/200	Blade shape: backward	Foot: existent	Flange: existent	Noise free bearing: yes
C₄	50	76	B35	Material: QP–1/200	Blade shape: forward	Foot: existent	Flange: existent	Noise free bearing: no
C₅	50	68	B35	Material: QP–1/200	Blade shape: forward	Foot: existent	Flange: existent	Noise free bearing: yes
C₆	5–50	76	B35	Material: QP–2/200	Blade shape: forward	Foot: existent	Flange: existent	Noise free bearing: no
C₇	5–50	68	B5	Material: QP–2/200	Blade shape: forward	Foot: nonexistent	Flange: existent	Noise free bearing: yes
C₈	5–50	56	B35	Material: QP–2/200	Blade shape: backward	Foot: existent	Flange: existent	Noise free bearing: no
C₉	5–50	68	B3	Material: QP–2/200	Blade shape: backward	Foot: existent	Flange: nonexistent	Noise free bearing: no
C₁₀	5–50	56	B5	Material: QP–2/200	Blade shape: backward	Foot: nonexistent	Flange: existent	Noise free bearing: no

RF: rated frequency; N: noise; MA: mounting arrangement; SW: stator windings; FA: fan; FR: frame; EC: end covers; B: bearings.

For simplicity, 10 cases are selected for the example. The information in the table is only a sample of the complete case list, for brevity. The information for different cases, which is not listed in the table, is identical. The number of attributes that are not listed in the table is 65. In this example, because there are only 10 cases, the support threshold is set at 5% and the confidence threshold is set at 60%.Using the adaptation rule acquisition method in section “Adaptation rule acquisition,” the adaptation rules are acquired. The acquired rules and their support and confidence are shown in Table 2.

Table 2.

The acquired adaptation rules.

Number	Antecedent	Consequent	Support	Confidence
R₁	The rate frequency changes from 50 Hz to 5–50 Hz	Change the stator windings from QP–1/200 to QP–2/200	0.278	1
R₂	The rate frequency changes from 5–50 Hz to 50 Hz	Change the stator windings from QP–2/200 to QP–1/200	0.278	1
R₃	The mounting arrangement changes from B3 to B5	Remove the foot of the frame and add flange to the end cover	0.067	1
R₄	The mounting arrangement changes from B5 to B3	Add foot to the frame and remove the flange of the end cover	0.067	1
R₅	The mounting arrangement changes from B3 to B35	Add flange to the end cover	0.111	1
R₆	The mounting arrangement changes from B35 to B3	Remove the flange of end cover	0.111	1
R₇	The mounting arrangement changes from B5 to B35	Add foot to the frame	0.167	1
R₈	The mounting arrangement changes from B35 to B5	Remove the foot of the frame	0.167	1
R₉	The noise changes from 56 to 68 dB	Change the fan from backward to forward	0.111	0.667
R₁₀	The noise changes from 68 to 56 dB	Change the fan from forward to backward	0.111	0.667
R₁₁	The noise changes from 56 to 76 dB	Change the fan from backward to forward and change the noise-free bearing to a normal one	0.111	1
R₁₂	The noise changes from 76 to 56 dB	Change the fan from forward to backward, and change the normal bearing to a noise-free one	0.111	1

The weights of the design requirements are obtained using equation (4). The design requirements of the new design task are shown in Table 3.

Table 3.

New design requirements.

RF (Hz)	N (dB)	MA
5–50	68	B35

RF: rated frequency; N: noise; MA: mounting arrangement.

According to the similarity evaluation method, the case most similar to the target case is C₅.

The difference between the design requirements of the target case and C₅ is in RF. Rule R₁ matches the changing event “The rate frequency changes from 50 Hz to 5 ∼ 50 Hz.” According to R₁, the material of the stator windings of C₅ should be changed from QP–1/200 to QP–2/200.

Experiments

Objective and data source

Two experiments were performed to investigate whether the proposed method can achieve higher adaptation performance compared with other methods. The proposed method is compared with two machine learning methods of adaptability-involving support vector machine (ASVM)¹³ and radial basis function network (RBFN),¹⁰ and a statistical method of WM.¹⁴ A detailed description of ASVM, RBFN, and WM methods is given later. ASVM is implemented using the LIBSVM tool.²⁷ Apriori and RBFN are implemented using the WEKA library, which includes a set of machine learning algorithms.²⁸ A total of 300 electromotor cases from company N were collected as raw data. The main product of the company is an electromotor. The production mode of the company is multivariety and small batch. The support threshold was set at 2%. The confidence threshold was set at 40%.

Comparative methods

ASVM

The basic idea of using ASVM for adaptation is to perform a regression approximation that addresses the problem of estimating a function to model the associative relations between the input $x_{i}$ and the output $y_{i}$ . ASVM approximates the unknown function with the form $f (x) = ω^{T} φ (x) + β$ , where ${φ (x)}_{i = 1}^{n}$ is the high-dimensional feature space, which is nonlinearly mapped from the input space. ${ω}_{i = 1}^{n}$ and $β$ are the normal vector and the bias and are estimated by minimizing

$R (ω) = C \frac{1}{n} \sum_{i = 1}^{n} L_{ε} (y_{i}, f (x_{i})) + \frac{1}{2} ∥ ω ∥^{2}$ (7)

$L_{ε} (y_{i}, f (x_{i})) = {\begin{matrix} | y_{i} - f (x_{i}) | - ε, & | y_{i} - f (x_{i}) | > ε \\ 0, & otherwise \end{matrix}$ (8)

According to previous work,¹³ the kernel function, ε and C are assigned as the radial basis kernel, 0.01 and 1000.

RBFN

The method adopts RBFN to realize case adaptation¹⁰

$f (x) = \sum_{i = 1}^{n_{h}} Φ (V_{i}) w_{i} + err$ (9)

Equation (9) describes the RBFN-employing adaptation knowledge application process where f(x) is the inference value, $n_{h}$ is the number of neurons in the hidden layer (as determined by the number of representative cases), err is the error, $w_{i}$ is the weight between the ith hidden layer and the output layer, and $Φ (V_{i})$ is the radial basis function. In the experiments, $n_{h}$ is set to 11 based on the suggestion of the designers of company N.

WM

The method obtains the design results by calculating the weighted average value of the same attribute of the k nearest previous cases, as shown in equation (10)

$rsv' = \frac{\sum_{i = 1}^{k} rs v_{i} \times S R_{i}}{k \sum_{j = 1}^{k} S R_{j}}$ (10)

where $rsv'$ and $rs v_{i}$ are the one design result values of new design and the ith retrieved case, respectively. $S R_{i}$ is the similarity between the new design and the ith retrieved case. In the experiments, k is set at 9 according to a previous article.¹⁴

Validation technique

The 10-fold cross-validation technique²⁹ was adopted to compare the performance of different adaptation methods. The cases were randomly divided into 10 groups, with the same size, in every experiment. One group was used as a test fold, and the other nine groups were used to train the adaptation models. The mean absolute percentage error (MAPE) was used to measure the differences between the adapted values and the actual values of the test cases. MAPE was obtained using equation (11)

$MAPE = \frac{1}{10 n_{r} n_{f}} \sum_{k = 1}^{10} \sum_{i = 1}^{n_{f}} \sum_{j = 1}^{n_{r}} \frac{| ta {v'}_{j} - ta v_{j} |}{ta v_{j}}$ (11)

where $n_{r}$ is the number of the design result attributes, $n_{f}$ is the number of cases in one group, $ta v'_{j}$ is the adapted value of the jth attributes, and $ta v_{j}$ is the actual value of the jth attribute.

Experiment 1

In this experiment, the performance of the different methods was compared in case bases with sizes of 100, 150, 200, 250, and 300. The design requirements and design results included both numerical and categorical attributes. The design requirements included the RP, RV, NP, power factor, efficiency factor, PC, CM, and MA. The design results included the slot shape of the stator, the slot number, the frame diameter, the frame bore, the material of the stator core, the material of the stator coil, the rotor bars, the rotor major diameter, the rotor minor diameter, the material of the RC, the material of the rotor coil, and the axial length. For the ASVM, RBFN, and WM methods, the values of categorical attributes were mapped to numbers. The adapted values were rounded to the nearest integer.

As shown in Figure 3, our method outperformed other methods. The superiority became greater as the data scale became larger.

Figure 3.

The performance of different methods with different data scales.

Experiment 2

In this experiment, the performance of the methods was compared with and without categorical attributes. The number of cases was set at 300. The MAPE of experiment 1, when the case number was 300, was used as the performance of the methods with categorical attributes. For the situation without categorical attributes, the design requirements included RP, RV, NP, power factor, efficiency factor, and the design result included slot number, frame diameter, frame bore, material of stator core, rotor bars, rotor major diameter, rotor minor diameter, and axial length.

As shown in Figure 4, ASVM and our method had the same performance when the design requirements and design results had only numerical attributes. However, our method outperformed other methods when the design requirements and design results had both numerical and categorical attributes.

Figure 4.

The performance of different methods with and without categorical attributes.

Conclusion and future work

A method of case adaptation for variant design was proposed in this study. A technique of data mining was introduced to acquire the adaptation rules that reflect the relationship between the changes in design requirements and design results. First, the raw data are encoded. Then, the changing events are extracted by case comparison. Finally, the adaptation rules are acquired using the Apriori algorithm. In the case retrieval process, the design requirements are weighted by analyzing the adaptation rules. The most similar case is selected by similarity evaluation. In the case adaptation process, the suitable rules are selected by analyzing their support and confidence. Then, the adaptation inference is realized based on the selected rules. Finally, the inference result is decoded to accomplish the variant design. Two experiments are performed to validate the proposed method. The results show that our method outperforms other methods when the design requirements and design results have both numerical and categorical attributes.

In the discretization of numerical attributes of this study, the values of attributes are discretized by equal-width binning. A better discretization method may improve the accuracy of the adaptation rules. Thus, we will try other discretization methods in future work.

Footnotes

Handling Editor: Filippo Berto

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This work was supported by the Nature Science Foundation of China (51375277) and the Shandong Provincial Natural Science Foundation of China (ZR2012GM015).

References

Congqian

Weixin

. Research on assembly modelling for product variant design. Chin J Mech Eng 2004; 30: 38–42.

Liu

. Joint optimization of complex product variant design responding to customer requirement changes. J Intel Fuzzy Syst 2016; 30: 397–408.

Schank

. Dynamic memory: a theory of reminding and learning in computers and people. Cambridge: Cambridge University Press, 1983.

Liao

Mao

Hannam

et al . Adaptation methodology of CBR for environmental emergency preparedness system based on an improved genetic algorithm. Expert Syst Appl 2012; 39: 7029–7040.

Yip

AYN

. Predicting business failure with a case-based reasoning approach. In: International conference on knowledge-based intelligent information and engineering systems, Wellington, New Zealand, 20–25 September 2004, pp.665–671. Berlin: Springer.

Darder

Valera

Nieto

et al . Multisensor device based on case-based reasoning (CBR) for monitoring nutrient solutions in fertigation. Sensor Actuat B: Chem 2009; 135: 530–536.

Biermans

MCJ

De Bakker

Verheij

et al . Development of a case-based system for grouping diagnoses in general practice. Int J Med Inform 2008; 77: 431–439.

Krovvidy

Wee

. Wastewater treatment systems from case-based reasoning. Mach Learn 1993; 10: 341–363.

De Paz

Bajo

González

et al . Combining case-based reasoning systems and support vector regression to evaluate the atmosphere–ocean interaction. Knowl Inf Syst 2012; 30: 155–177.

10.

Jung

Lim

Kim

. Integrating radial basis function networks with case-based reasoning for product design. Expert Syst Appl 2009; 36: 5695–5701.

11.

Zhu

. Product design pattern based on big data-driven scenario. Adv Mech Eng 2016; 8: 1–9.

12.

Tong

Kwong

Chan

. Process design for transfer moulding of electronic packages using a case-based reasoning approach with fuzzy regression adaptation. Int J Comput Integ M 2005; 18: 27–40.

13.

Peng

. Incorporating adaptability-related knowledge into support vector machine for case-based design adaptation. Eng Appl Artif Intel 2015; 37: 170–180.

14.

Peng

. New CBR adaptation method combining with problem–solution relational analysis for mechanical design. Comput Ind 2015; 66: 41–51.

15.

Vong

Leung

Wong

. Case-based reasoning and adaptation in hydraulic production machine design. Eng Appl Artif Intel 2002; 15: 567–585.

16.

Janthong

Brissaud

Butdee

. Combining axiomatic design and case-based reasoning in an innovative design methodology of mechatronics products. CIRP J Manuf Sci Technol 2010; 2: 226–239.

17.

et al . Adaptation rule learning for case based reasoning. Concurr Comp: Pract E 2009; 21: 673–689.

18.

Hong

Han

. Knowledge-based data mining of news information on the Internet using cognitive maps and neural networks. Expert Syst Appl 2002; 23: 1–8.

19.

Götz

García-Gómez

Terol

et al . High-throughput functional annotation and data mining with the Blast2GO suite. Nucleic Acids Res 2008; 36: 3420–3435.

20.

Kantety

La Rota

Matthews

et al . Data mining for simple sequence repeats in expressed sequence tags from barley, maize, rice, sorghum and wheat. Plant Mol Biol 2002; 48: 501–510.

21.

Walker

Kadam

. Predicting breast cancer survivability: a comparison of three data mining methods. Artif Intel Med 2005; 34: 113–127.

22.

Huang

Chen

Wang

. Credit scoring with a data mining approach based on support vector machines. Expert Syst Appl 2007; 33: 847–856.

23.

Chaves

Ramírez

Górriz

. Integrating discretization and association rule-based classification for Alzheimer’s disease diagnosis. Expert Syst Appl 2012; 40: 1571–1578.

24.

Agrawal

Imieliński

Swami

. Mining association rules between sets of items in large databases. SIGMOD Rec 1993; 22: 207–216.

25.

Agrawal

Srikant

. Fast algorithms for mining association rules in large databases. In: Proceedings of the 20th international conference on very large data bases (VLDB ’94), Santiago, Chile, 12–15 September 1994, pp.487–499. San Francisco, CA: Morgan Kaufmann Publishers.

26.

Lazcorreta

Botella

Fernández-Caballero

. Towards personalized recommendation by two-step modified Apriori data mining algorithm. Expert Syst Appl 2008; 35: 1422–1429.

27.

Chang

Lin

. LIBSVM: a library for support vector machines. ACM T Intel Syst Tec 2011; 2: 27.

28.

Witten

Frank

. Data mining: practical machine learning tools and techniques. 2nd ed. Burlington, MA: Morgan Kaufmann, 2005.

29.

Demsar

. Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 2006; 7: 1–30.

A method of case adaptation for variant design integrating data mining