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The lightweight design of autobody involves multiple objectives and requires the collaboration between various disciplines. To improve the existing autobody lightweight designs, it is necessary to establish an accurate and objective evaluation method for lightweight effect. This paper proposes an extension decision tree (EDT) algorithm for lightweight design of autobody. The algorithm solves the contradictions in the autobody lightweight design were solved through divergence and convergence. The workflow of the solving process is shaped like a scalable diamond. Specifically, the knowledge of autobody structure was described accurately by extension modeling and extension divergence reasoning. Then, the lightweight design of autobody structure and material was achieved through extension transforms. Next, the EDT algorithm was constructed based on extension theory and the DT algorithm, and used to evaluate the lightweight effect of autobody. Finally, the effectiveness of the proposed algorithm as verified through a case study and a computeraided engineering (CAE) simulation. The results show that our algorithm can accurately predict the weight reduction effect of autobody based on the case data, and generate a set of intelligent strategies to optimize the current design. The research results shed new light on intelligent evaluation of autobody lightweight design with multiple objectives and constraints.
autobody lightweight design, extension model, divergence reasoning, extension transform, extension decision tree (EDT) model
With the upgrading of industrial structure and the promotion of green policies, the market share of new energy vehicles is growing year by year. Compared with traditional cars, new energy vehicles consume a limited amount of energy, create a few noises and cause no pollution [1, 2]. However, the popularity of new energy vehicles has been limited by the short cruising range. The cruising range can be improved through lightweight design of autobody, which accounts for much of the weight of the vehicle [37]. In fact, the lightweight design of autobody needs to achieve multiple objectives through the collaboration between various disciplines. In addition to reducing the autobody weight, the designer must consider an array of vehicle features, including mechanical properties, process difficulty, and production cost. This calls for a complete and objective method to evaluate the lightweight effect of autobody design [810].
Many scholars have attempted to reduce the weight of autobody. For instance, Sorenson et al. [11] optimized the sound transmission loss of lightweight autobody structure by balancing the surface density between sheet metal and the barrier. From the environmental perspective, Mayyas et al. [12] assessed different lightweight designs and electric powertrains through a lifecycle analysis on energy cost and CO2 emissions, shedding light on the combined effect of lightweight and electrification. Based on analytical drive design, Lv et al. [13] put forward a lightweight multiobjective optimization method for closed body in white (BIW), which effectively reduces the mass of closed BIW and improves the lightweight rate. Wang et al. [14] developed a lightweight design of the BIW based on implicit parametric model, which reduces the weight of the autobody without sacrificing its static and dynamic performance. However, the above studies have not fully disclosed the implicit relationship between the materials of autobody structure and the multiple objectives/constraints of lightweight design, failing to explore knowledge representation or reasoning. The development of the information technology and computer technology has created a large amount of knowledge in carboy design on the Internet, laying a good basis for the evaluation of lightweight effect of autobody design.
The decision tree (DT) is a popular classification and prediction algorithm [1519]. The DT can extract the relationship between data features and classes in a set of disordered, irregular cases, and, on this basis, classify the current data in an accurate manner [2023]. Therefore, the DT has been widely used for multifeature index evaluation. For example, Khedr et al. [24] improved the Iterative Dichotomiser 3 (ID3) algorithm for DT learning, based on data partitioning and parallelism. Cherfi et al. [25] presented the very fast C4.5 (VFC4.5) DT algorithm, which outperformed the very fast DT (VFDT) algorithm in building DTs. To achieve image population density classification, Wang et al. [26] proposed a multiclass classification method based on the DT, support vector machine (SVM) and particle swarm optimization (PSO). Han et al. [27] designed a frequent mode DT for processing variable data streams, which greatly improves the processing accuracy of data streams in the steady state. The DT enjoys can classify and predict the case data well. If the prediction effect falls short of the design requirements, however, it is impossible for the DT to generate a new intelligent design. To solve the problem, the extension theory has been introduced to develop an extension DT (EDT) algorithm.
The extension theory mainly studies the possibility of expanding things with a formal model, providing new insights into the intelligent solution to contradictions. The expansion is achieved through methods called extension transform. The EDT algorithm merges the extension transform with the DT seamlessly: whenever the prediction effect of the DT falls short of the design requirements, the extension strategy will be generated. The EDT algorithm has a good application prospect in casebased design. Guo and Zou [28] created a building planning prediction method based on DT classification, which promotes the computeraided extension in building planning. Wen and Li [29] put forward an ontology knowledge expansion analysis tree and improved the extension strategy generation system. Overall, the research on the EDT algorithm concentrates on the elementary transformation theory of extension transform. There is no report on the construction of the primitive model or the realization of the extension thinking mode.
In the light of extension modelling, extension reasoning, extension transform and the DT, this paper aims to evaluate the lightweight effect of multiobjective autobody design, which is achieved through the collaboration of various disciplines, and disclose the implicit relationship between the materials of autobody structure and the multiple objectives/constraints of lightweight design, using the case data from the Internet. The most significant contribution is the design of an EDT algorithm for the lightweight design of autobody. Firstly, the autobody parts and joining technology were described with matterelement model and relationelement model, respectively, and diverged based on the divergence rules of multiple objects and features, providing the knowledge of the autobody structure. Next, the ID3 algorithm was combined with extension transform to accurately evaluate the lightweight effect and generate new design strategies, solving the contradictions in lightweight effect prediction. Furthermore, the authors developed a calculation model for extension transform difficulty, which overcomes combination explosion, eliminates redundant solutions, and identifies the optimal extension strategy. Finally, a computeraided engineering (CAE) simulation was conducted to verify the mechanical properties (e.g. torsional stiffness and bending stiffness) of the autobody optimized by our EDTbased design. The research results help to improve the autobody weight under multiple constraints.
2.1 Primitive modeling and divergence reasoning for autobody structure knowledge
A huge amount of knowledge is involved in the lightweight design of autobody. There is the dynamic knowledge about design actions (e.g. structural optimization, material replacement and performance improvement), the static knowledge about object properties (e.g. autobody parts, technological types and material property), and the relational knowledge between different things (e.g. the joining technology for components).
The different types of knowledge must be described accurately in the design process. Therefore, the concept of extension primitives was introduced to illustrate the autobody structure by matterelement model and relationelement model. The autobody structure was divided into autobody parts and joining technology. The autobody parts include the BIW, decorative part, covering part, chassis part, etc., while the joining technology consists of welding, mechanical assembly, bonding, etc.
Regarded as static knowledge, the autobody parts were described by the matterelement model $M=(O m, C m, V m)$ where $O m$ is the name of the autobody part, $C m$ is the feature, and $V m$ is the interval of the feature. According to the divergence rules of multiple objects and features, the object $O m$ was diverged into $O m=[O m 1, O m 2, O m 3, O m 4 \ldots]$, where $O m i$ is one of the autobody parts, namely, the BIW, decorative part, covering part, and chassis part, while the feature $\quad \mathrm{Cm} \quad$ was $\quad$ diverged $\quad$ into $\quad \mathrm{Cm}=$ $[\mathrm{Cm} 1, \mathrm{Cm} 2, \mathrm{Cm} 3, \mathrm{Cm} 4 \ldots]$, where $Cmi$ is one of the features, namely, the component weight, material property and cost. Then, the divergence tree for the matterelement model $M$ of the static knowledge can be established as:
$M\mapsto \left\{ \begin{matrix} \text{M1}=\left[ \begin{matrix} {{O}_{m1}} & {{C}_{m11}} & {{V}_{m11}} \\ {} & {{C}_{m12}} & {{V}_{m12}} \\ {} & ...... & ...... \\ {} & {{C}_{m1i}} & {{V}_{m1i}} \\\end{matrix} \right]=\left[ \begin{matrix} \text{ }BIW\text{ } & component\text{ }weigh{{t}_{11}} & \text{ }valu{{e}_{11}} \\ {} & material\text{ }propertie{{s}_{12}} & \text{ }valu{{e}_{\text{12}}} \\ {} & ...... & ...... \\ {} & cos{{t}_{\text{1}i}} & \text{ }valu{{e}_{\text{1}i}} \\\end{matrix} \right] \\ \text{M2}=\left[ \begin{matrix} {{O}_{m2}} & {{C}_{m21}} & {{V}_{m21}} \\ {} & {{C}_{m22}} & {{V}_{m22}} \\ {} & ...... & ...... \\ {} & {{C}_{m2i}} & {{V}_{m2i}} \\\end{matrix} \right]=\left[ \begin{matrix} \text{ }decorative\text{ }part & component\text{ }weigh{{t}_{21}} & valu{{e}_{21}} \\ {} & material\text{ }propertie{{s}_{22}} & valu{{e}_{22}} \\ {} & ...... & ...... \\ {} & cos{{t}_{2i}} & valu{{e}_{2i}} \\\end{matrix} \right] \\ \text{M3}=\left[ \begin{matrix} {{O}_{m\text{3}}} & {{C}_{m\text{3}1}} & {{V}_{m\text{3}1}} \\ {} & {{C}_{m\text{3}2}} & {{V}_{m\text{3}2}} \\ {} & ...... & ...... \\ {} & {{C}_{m\text{3}i}} & {{V}_{m\text{3}i}} \\\end{matrix} \right]=\left[ \begin{matrix} \text{ }covering\text{ }part\text{ } & component\text{ }weigh{{t}_{\text{3}1}} & valu{{e}_{\text{3}1}} \\ {} & material\text{ }propertie{{s}_{\text{3}2}} & valu{{e}_{\text{3}2}} \\ {} & ...... & ...... \\ {} & cos{{t}_{\text{3}i}} & valu{{e}_{\text{3}i}} \\\end{matrix} \right] \\ \text{M4}=\left[ \begin{matrix} {{O}_{m\text{4}}} & {{C}_{m\text{4}1}} & {{V}_{m\text{4}1}} \\ {} & {{C}_{m\text{4}2}} & {{V}_{m\text{4}2}} \\ {} & ...... & ...... \\ {} & {{C}_{m\text{4}i}} & {{V}_{m\text{4}i}} \\\end{matrix} \right]=\left[ \begin{matrix} \text{ }chassis\text{ }part\text{ } & component\text{ }weigh{{t}_{\text{4}1}} & valu{{e}_{\text{4}1}} \\ {} & material\text{ }propertie{{s}_{\text{4}2}} & valu{{e}_{\text{4}2}} \\ {} & ...... & ...... \\ {} & cos{{t}_{\text{4}i}} & valu{{e}_{\text{4}i}} \\\end{matrix} \right] \\\end{matrix} \right.$ (1)
Regarded as relational knowledge, the joining technology was described by the relationelement model $R=$ $(O r, C r, V r),$ where $O r$ is the name of the joining technology, $C r=[C r 1, C r 2, C r 3]$ is the feature of the joining technology, and $V=[\text {Vr1}, \text {Vr2,Vr3,Vr4}]$ is the interval of the feature. According to the divergence rules of multiple objects and features, the object O $m$ was diverged into [Or1, Or2, Or3...], where Ori is one of the components of the joining technology, namely, welding, bonding and mechanical assembly, while the feature $C r=[C r 1, C r 2, C r 3] \quad$ was $\quad$ diverged into $\quad C r=$ $[\mathrm{Cr} 1, \mathrm{Cr} 2, \mathrm{Cr} 3 \ldots .],$ where $\mathrm{Cr} i$ is one of the features, namely, into technology difficulty, connection quality, and positional relationship. Then, the divergence tree for the relationelement model $R$ of the relational knowledge can be established as:
$R\mapsto \left\{ \begin{matrix} \text{R1}=\left[ \begin{matrix} {{O}_{R1}} & {{C}_{R11}} & {{V}_{R11}} \\ {} & {{C}_{R12}} & {{V}_{R12}} \\ {} & ...... & ...... \\ {} & {{C}_{R1i}} & {{V}_{R1i}} \\\end{matrix} \right]=\left[ \begin{matrix} \text{ }welding\text{ } & \ \ \ \ \ technology\text{ }difficult{{y}_{11}} & \text{ }valu{{e}_{11}} \\ {} & \ \ \ \ \ connection\text{ }qualit{{y}_{12}} & \text{ }valu{{e}_{\text{12}}} \\ {} & ...... & ...... \\ {} & \ \ \ \ positional\text{ }relationshi{{p}_{\text{1}i}} & \text{ }valu{{e}_{\text{1}i}} \\\end{matrix} \right] \\ \text{R1}=\left[ \begin{matrix} {{O}_{R1}} & {{C}_{R21}} & {{V}_{R21}} \\ {} & {{C}_{R22}} & {{V}_{R22}} \\ {} & ...... & ...... \\ {} & {{C}_{R2i}} & {{V}_{R2i}} \\\end{matrix} \right]=\left[ \begin{matrix} \text{ }bonding\text{ } & \ \ \ \ \ technology\text{ }difficult{{y}_{\text{2}1}} & valu{{e}_{\text{2}1}} \\ {} & \ \ \ \ \ connection\text{ }qualit{{y}_{\text{2}2}} & valu{{e}_{\text{22}}} \\ {} & ...... & ...... \\ {} & \ \ \ \ \ \ positional\text{ }relationshi{{p}_{\text{2}i}} & valu{{e}_{\text{2}i}} \\\end{matrix} \right] \\ \text{R1}=\left[ \begin{matrix} {{O}_{31}} & {{C}_{R31}} & {{V}_{R31}} \\ {} & {{C}_{R32}} & {{V}_{R32}} \\ {} & ...... & ...... \\ {} & {{C}_{R3i}} & {{V}_{R3i}} \\\end{matrix} \right]=\left[ \begin{matrix} mechanical\text{ }assembly & technology\text{ }difficult{{y}_{\text{3}1}} & valu{{e}_{\text{3}1}} \\ {} & connection\text{ }qualit{{y}_{\text{3}2}} & valu{{e}_{\text{32}}} \\ {} & ...... & ...... \\ {} & positional\text{ }relationshi{{p}_{\text{3}i}} & valu{{e}_{\text{3}i}} \\\end{matrix} \right] \\\end{matrix} \right.$ (2)
Based on formulas (1) and (2), the matterelement model M of autobody parts and the relationelement model R of the joining technology can be obtained, respectively.
In this way, the autobody knowledge can be described accurately from the aspects of the object, the feature, the feature quantity, etc. Drawing on extension theory, the primitive model B of the autobody structure can be established as:
$B=({{M}_{1}}\oplus {{M}_{2}}\oplus {{M}_{3}}\oplus {{M}_{4}})\oplus ({{R}_{1}}\oplus {{R}_{2}}\oplus {{R}_{3}})$ (3)
where, M_{1}~_{4} are the models of the BIW, the decorative part, the cover part and the chassis part, respectively; R_{1~3 }are the models of welding, bonding and mechanical assembly, respectively. Based on formula (3), an entityrelationship (ER) model can be constructed for the knowledge of autobody design (Figure 1).
Figure 1. The ER model of the knowledge of autobody design
2.2 Optimization of lightweight material and structure through extension transforms
There are two aspects of autobody lightweight design: the lightweight design of material and the lightweight design of structure. The former reduces the weight of the autobody by using lightweight materials, and the latter reduces the number of parts through structural optimization. Following the principle of extension reasoning, a desirable lightweight design should be prepared by extending the design ideas through transforms like displacement, addition, deletion, expansion, contraction and decomposition.
The material lightweight technology, which pursues weight reduction by material replacement, can be expressed as a displacement transform $T_{1} \Gamma=\Gamma^{\prime};$ $\quad$ where, $\quad T_{1}$ is the displacement transform, $\Gamma$ is the original material and $\Gamma^{\prime}$ is the transformed material. According to the different properties of the transformed material $\Gamma^{\prime},$ the displacement transform $T_{1}$ can be diverged into highstrength steel transform $T_{11},$ ultrahighstrength steel transform $T_{12},$ aluminum alloy transform $T_{13},$ magnesium alloy transform $T_{14},$ composite material transform $T_{15},$ etc.
The structural lightweight technology, which pursues weight reduction through structural optimization and material reduction, can be expressed as a deletion transform $T_{2} \Gamma=$ $\Gamma \Theta \Gamma^{\prime},$ where $T_{2}$ is the deletion transform, $\Gamma$ is the original structure and $\Gamma^{\prime}$ is the transformed structure. According to different design methods, the deletion transform $T_{2}$ can be diverged into size transform $T_{21},$ topography transform $T_{22}$ topological transform $T_{23},$ etc.
Based on the above two technologies, the divergence tree for the autobody lightweight design can be established as:
$T\mapsto \left\{ \begin{matrix} \text{ }T1\mapsto \left\{ \begin{matrix} T11=Highstrength\text{ }steel\text{ }transform \\ T12=Ultrahighstrength\text{ }steel\text{ }transform\text{ } \\ T13=Alu\text{min}um\text{ }alloy\text{ }transform\text{ } \\ T14=Magnesium\text{ }alloy\text{ }transform \\ T15=Composite\text{ }material\text{ }transform \\\end{matrix} \right. \\ T2\mapsto \left\{ \begin{matrix} T21=Size\text{ }transform \\ \text{ }T22=Topography\text{ }transform \\ \text{ }T23=Topo\text{log}ical\text{ }transform \\\end{matrix} \right. \\\end{matrix} \right.$ (4)
As shown in formula (4), the autobody lightweight design $T$ can be diverged into highstrength steel transform $T_{11},$ ultrahighstrength steel transform $T_{12},$ aluminum alloy transform $T_{13},$ magnesium alloy transform $T_{14},$ composite material transform $T_{15},$ size transform $T_{21},$ topography transform $T_{22}$, topological transform $T_{23},$ etc. In this way, the lightweight design is accurately described in terms of material property and autobody structure. From the perspective of extension, the extension transform of the autobody lightweight design $T$ can be established as:
$T=T1\oplus T2=(T11\oplus T12\oplus T13\oplus T1\text{4}\oplus T1\text{5})\oplus (T21\oplus T22\oplus T23)$ (5)
2.3 Extension decision tree model for autobody lightweight design
The DT is a treelike prediction model, in which the conditional probability distribution is defined by the branch structure on the feature space. As a result, the DT can find the relationship between the features and classes in a set of disordered, irregular cases, and predict the class of new data based on features. Despite being extensively applied in effect prediction, the traditional DT model cannot generate new designs if the current design fails to satisfy the requirements. Therefore, it is necessary to create a new DT model that effectively integrates effect prediction with strategy generation.
The EDT model seamlessly merges the DT model and the extension strategy generation. Specifically, the DT model is used to predict the design effect. If the original strategy falls short of the demand, the extension transform is performed to generate a new strategy. In autobody lightweight design, the EDT model consists of several parts, namely, the construction of competitive products database, primitive modeling and divergence reasoning of autobody structure, classification and prediction of ID3 algorithm, to name but a few.
(1) The construction of competitive products database
Perform competitive products analysis on the massive data of the Internet of Things (IoT). Through the analysis, collect the weight, performance, size, price and other parameters from various models. Next, select the competitive products with similar positioning of the current product, and evaluate the lightweight effect of these products. Then, obtain the parameters of the autobody parts, joining technology, weight, cost and lightweight effect of the competitive products, and consolidate them into a competitive products database.
(2) Primitive modelling and divergence reasoning of autobody structure
Build a knowledge model of autobody structure based on the concept of extension primitives. Taking the autobody parts as static knowledge, construct the matterelement model of autobody parts like the BIW, decorative part, covering part and chassis part, diverge the model into submodels of each part according to the divergence rules of multiple objects and features, and import related data from the bill of materials (BOM). Taking the joining technology as relational knowledge, build the relationelement model of processes like welding, bonding and mechanical assembly, diverge the model into submodels of each process according to the divergence rules of multiple objects and features, and import related data from the bill of materials (BOM).
(3) The classification and prediction of ID3 algorithm
The DT is a treelike classification algorithm. According to information theory, the DT algorithm can be categorized into the ID3 algorithm, C4.5 algorithm, classification and regression tree (CART) algorithm, etc. Among them, the ID3 algorithm relies on the information gain of information theory for feature selection. In each iteration, a topdown search is performed through the decision space to select the feature with the largest information gain for splitting. Compared with the other DT algorithms, the ID3 algorithm is fast and easy to use, and thus widely adopted for data mining. Therefore, this algorithm is selected here for decision reasoning, which covers the following steps:
Step 1. Calculation of information entropy of a random variable
Let $X=\left\{X_{1}, X_{2}, \cdots, X_{n}\right\}$ be a random variable containing $n$ samples, and $P=\left\{P_{1}, P_{2}, \cdots, P_{n}\right\}$ be the probability of occurrence of each sample. Then, the information entropy of variable $X$ can be computed by:
$I(X)=\sum\limits_{i=1}^{n}{{{P}_{i}}}{{\log }_{2}}{{P}_{i}}$ (6)
As shown in formula (6), the system instability is positively correlated with the number of uncertain factors within the random variable $X$. In other words, the greater the information entropy, the more the information required to make a clear description of the random variable.
Step 2. Calculation of information entropy of the classification system
Let $A=\left\{A_{1}, P A_{2}, \cdots, A_{m}\right\}$ be a feature of the classification system, and $P=\left\{P\left(A_{1}\right), P\left(A_{2}\right), \cdots, P\left(A_{m}\right)\right\} \quad$ be the probability of occurrence for each class. The sample data can be classified by feature $A .$ Then, the information entropy of the classification system can be computed by:
$I(A)=\sum\limits_{i=1}^{\text{m}}{P({{A}_{i}})}{{\log }_{2}}P({{A}_{i}})$ (7)
Step 3. Calculation of information gain
The information gain refers to the information entropy difference between a random variable and the classification system. The information gain can be computed by:
$G(A)=I(X)I(A)$ (8)
The greater the information gain, the more important the feature is to the decisionmaking process.
Step 4. Creation of a complete DT model
Select the feature with the largest information gain as the split node, and represent each “parentchild” path in the “if…then” form. Moreover, traverse the possible decision space, and classify the static, dynamic, and relational knowledge contained in the design, creating a complete DT model.
Step 5. Judgement of the necessity to generate a new design
Substitute the primitive model of the current design into the DT algorithm, and determine the features of each subnode branch. If it satisfies the design requirements, take the current design as the optimal solution; otherwise, extend the autobody parts model and the joining technology model, and construct the divergence tree model to generate a new design.
Step 6. Optimization of lightweight material and structure through extension transforms
If the current lightweight design is predicted to fall short of the demand, perform extension transforms to generate a new strategy, including highstrength steel transform $T_{11},$ ultrahighstrength steel transform $T_{12},$ aluminum alloy transform $T_{13},$ magnesium alloy transform $T_{14},$ composite material transform $T_{15},$ size transform $T_{21},$ topography transform $T_{22}$ topological transform $T_{23},$ etc.
Step 7. Analysis of the difficulty in extension transform
According to the divergence rule of multiple objects and features, the divergence reasoning of the autobody structural element model $B$ and the autobody lightweight design $T$ are prone to combination explosion, which brings too many solution sets. To solve the problem, the concept of extension transform difficulty was introduced to select the optimal design for the convergence of design thinking. The extension transform difficulty can be computed as:
$extension\text{ }transform\text{ }difficulty=\prod{(transform\text{ }coefficient+\text{1)1}}$ (9)
where the transform coefficient is determined on a casebycase basis: If the features belong to different classes but fall on the same level in the material of lightweight design, type of connection process, etc., the transform coefficient should be set to 1 no matter how the transform is performed; if the features fall on different levels in terms like the lightweight effect, the transform coefficient should be set to 1, when the transform increases the features by one level, and set to 2, when the transform increases the features by two levels.
2.4 Implementation of extension decision tree algorithm
As shown in Figure 2, the EDT model for autobody lightweight design include the construction of competitive products database, primitive modeling and divergence reasoning of autobody structure, classification and prediction of ID3 algorithm, extension transforms based on material and structural lightweight technologies, analysis of extension transform difficulty, etc.
Figure 2. The EDT model for autobody lightweight design
The algorithm for the EDT model can be implemented in the following steps.
Step 1. Take multiple factors (e.g. weight, size, cost and mechanical properties) as reference indices, perform competitive products analysis to screen and extract the information of competitive products from a huge amount of data on the Internet, and consolidate the extracted information (e.g. weight, cost, process type, material property, autobody parts and lightweight effect) into a competitive products database.
Step 2. Construct the information gain calculation model based on formulas (6)(8). Then, set up the ID3 model with features (e.g. weight, cost, process type, material property and autobody parts) as nonleaf nodes, and lightweight effect as the leaf node. To ensure the modelling accuracy, divided the case data into a training set and a test set at the ratio of 3:1.
Step 3. Establish the autobody parts model, the joining technology model and the primitive model of autobody structure for the current design, according to formulas (1)(3), respectively. Then, construct the divergence tree of autobody structure according to the divergence rules of multiple objects and features, which can express the knowledge of autobody structure accurately from the aspects of object, feature and feature quantity.
Step 4. Substitute the primitive model of autobody structure into the ID3 model to classify and predict the lightweight effect of the current design. If the classification result meets the design requirements, jump to Step 7; otherwise, go to Step 5.
Step 5. Perform extension transforms (e.g. displacement transform, addition and deletion) to optimize the current autobody material and structure (formulas (4) and (5)), carry out divergent reasoning of lightweight design according to the divergence rules of multiple objects and features, and generate a set of new strategies with the aim to satisfy the design requirements.
Step 6. Calculate the difficulty in extension transform by formula (9) to evaluate the set of strategies, choose the least difficult extension strategy, and go back to Step 3.
Step 7. Conduct a CAE simulation to verify the mechanical properties (i.e. bending stiffness and torsional stiffness) of the current design. If these properties meet the design requirements, go to Step 8; otherwise, go back to Step 5.
Step 8. Select the current design as the optimal solution, and terminate the autobody lightweight design process.
As mentioned before, the autobody lightweight design needs to achieve multiple objectives and requires the collaboration between various disciplines. Besides the autobody weight, many other evaluation indices should be considered throughout the design process, including but not limited to the cost, type of process, material property, and mechanical properties. The evaluation indices being selected must be comprehensive, suitable and stable. Moreover, the indices should be classified to make the data accessible and the DT algorithm efficient. The easily accessible indices were classified to Level I and evaluated first. The typical Level I indices include weight, cost, process type, and material property, all of which are recorded in the BOM or process list. The indices that are hard to obtain (e.g. the mechanical properties can only be obtained through the CAE simulation) were allocated to Level II and evaluated later.
In this paper, the EDT algorithm for autobody lightweight design is established to judge the lightweight effect based on Level I indices like weight, cost, process type and material property. The specific steps of the algorithm are as follows:
Step 1. Selection of evaluation indices
Evaluate the lightweight effect of each competitive product through statistical analysis, challenge method, competitive analysis, etc. Divide the competitive products into excellent, medium and poor levels, and take the results as the outcomes of the DT. Then, set up the branches of the DT based on Level I indices like weight, cost, process type and material property. Finally, classify the features of the BIW by the DT.
Step 2. Construction of the DT model
Select 200 cases from the competitive product database to serve as data samples (Table 1).
Table 1. Data samples of competitive products
Serial number 
Parts name 
Joining technology 
Weight 
Material property 
Cost 
Lightweight effect 
1 
Covering part 
Mechanical assembly 
Substantially decreased 
Ⅰ Highstrength steel 
Medium 
Excellent 
2 
BIW 
Welding 
Substantially decreased 
Ⅲ Aluminum alloy 
Medium 
Medium 
3 
Decorative part 
Bonding 
Invariant 
Ⅴ Composite material 
Medium 
Poor 
4 
Chassis part 
Mechanical assembly 
Substantially decreased 
Ⅱ Ultrahigh strength steel 
Low 
Medium 
5 
Covering part 
Welding 
Invariant 
Ⅲ Aluminum alloy 
Low 
Poor 
... 
... 




... 
200 
Decorative part 
Mechanical assembly 
Slightly decreased 
IV Magnesium alloy 
Low 
Excellent 
After determining the evaluation indices and judgement result, divide the above data samples evenly into 20 parts, allocate 15 parts to the training set for constructing the DT model, and allocate the remaining 5 parts to the test set for verifying the model. An example of the DT model for autobody lightweight design is shown in Figure 3.
Step 3. Application of the DT model
Establish the autobody element model of the current design, and extract the Level I indices (e.g. weight, material property, process type, cost) from the model. Then, substitute the indices into the DT model to predict the lightweight effect of the design. If the design cannot meet the requirements, generate a new design strategy through extension transform.
Here, the current design is a lightweight design of the BIW, in which the weight is “Substantially decreased”, the material property is “III aluminum alloy”, the process type is “welding”, and the cost is “medium”. Then, the DT algorithm predicted that the lightweight effect is “general”, failing to meet the design requirements.
Figure 3. An example of the DT model for autobody lightweight design
Table 2. Sorting results of extension strategies
Serial number 
Extension Transform strategy 
Weight 
Material property 
Process type 
Cost 
Lightweight effect 
1 
$T_{11} \oplus T_{21}$ 
Substantially decreased 
Ⅰ Highstrength steel 
Mechanical assembly 
Medium 
Excellent 
2 
$T_{11} \oplus T_{22}$ 
Substantially decreased 
Ⅰ Highstrength steel 
Welding 
Low 
Excellent 
3 
$T_{12} \oplus T_{21}$ 
Slightly decreased 
Ⅱ Ultrahigh strength steel 
Welding 
Low 
Excellent 
4 
$T_{13} \oplus T_{21}$ 
Slightly decreased 
Ⅲ Aluminum alloy 
Mechanical assembly 
Medium 
Excellent 
… 
… 





Step 4. Generation of extension strategy
To achieve the “excellent” lightweight effect, perform extension transforms of lightweight material and structure of the autobody element model:
$\begin{align} & {{T}_{\text{11}}}\bullet {{M}_{1}}(BIW,Material,)={{M}_{1}}'(BIW,Material,) \\ & {{T}_{\text{12}}}\bullet {{M}_{1}}(BIW,Material,)={{M}_{1}}'(BIW,Material,) \\ & {{T}_{\text{13}}}\bullet {{M}_{1}}(BIW,Material,)={{M}_{1}}'(BIW,Material,) \\ & {{T}_{\text{14}}}\bullet {{M}_{1}}(BIW,Material,)={{M}_{1}}'(BIW,Material,) \\ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ... \\ & \\\end{align}$ (10)
Step 5. Sorting of extension strategies
Calculate the extension transform difficulty of each strategy generated through extension transforms, and sort the strategies by the difficulty in ascending order. The sorting results are shown in Table 2.
As shown in Table $2,$ the topranking strategy $T=T_{11}+T_{22}$ was selected as the optimal strategy. The BIW structure and implementation of the optimal strategy are displayed in Figure 4 and Table 3, respectively.
Step 6. The CAE simulation and results analysis
Perform a CAE simulation of the BIW, with bending stiffness and torsional stiffness as Level II evaluation indices. The simulation results are presented in Figures 5 and 6 and Table 4.
The simulation results show that the axial displacement, bending stiffness and torsional stiffness of the selected extension strategy met the design requirements. Hence, the autobody lightweight design process based on the EDT algorithm was terminated. The autobody lightweight design generated by the extension transforms is the optimal design to satisfy the design requirements.
Figure 4. The structure of the BIW
Table 3. Implementation of the optimal strategy
Extension transforms 
Lightweight method 
Lightweight location 
Process 
T11 
Lightweight material 
3/4 and 13 
Ordinary carbon steel →22MnB5 ultrahigh strength steel 
T21 
Lightweight structure 
11 and 12 
Round beam→Square beam 
Figure 5. The CAE results on bending stiffness
Figure 6. The CAE results on torsional stiffness
Table 4. The CAE results on bending stiffness and torsional stiffness
Type of load 
Load 
Zaxis displacement 
Bending stiffness 
Torsional stiffness 
Qualified? 
Axial force 
750 (N) 
0.073mm 
20,548 (N/mm) 
—— 
Yes 
Torque 
1,000 (N·m) 
1.04mm 
—— 
8671 (N·mm/deg) 
Yes 
This paper proposes an EDT algorithm for autobody lightweight design. Firstly, a matterelement model for autobody parts and a relationelement model for joining technology were established to accurately illustrate the knowledge about autobody structure. Next, the autobody structure was optimized and the autobody material was replaced through extension transforms for lightweight material and lightweight structure. Furthermore, an EDT algorithm for autobody lightweight design was constructed based on extension modeling, divergence inference and extension transform, and its implementation steps were explained in details. In this way, the contradictions in the autobody lightweight design were solved through divergence and convergence, generating an accurate prediction strategy for lightweight effect. The workflow of the solving process is shaped like a scalable diamond. The effectiveness and feasibility of the proposed algorithm were verified through a case study on the BIW lightweight design and the CAE simulation.
This research is supported by the National Natural Science Foundation of China (Grant No.: 51775272 and 51005114), and the Domestic Visiting and Training Program for Outstanding Young Talents in Colleges and Universities of Anhui Province, China (Grant No.: gxgnfx2019150).
[1] Wang, C.Q., Wang, D.F., Zhang, S. (2016). Design and application of lightweight multiobjective collaborative optimization for a parametric bodyinwhite structure. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of automobile engineering, 230(2): 273288. https://doi.org/10.1177/0954407015581937
[2] Liu, J.P., Wang, Z.H. (2018). Optimization of stamping process parameters for aluminum instead of steel based on orthogonal experiment. Journal of Plasticity Engineering, 5: 110116. https://doi.org/10.3969/j.issn.10072012.2018.05.015
[3] Hunkeler, S., Duddeck, F., Rayamajhi, M., Zimmer, H. (2013). Shape optimisation for crashworthiness followed by a robustness analysis with respect to shape variables. Structural and Multidisciplinary Optimization, 48(2): 367378. https://doi.org/10.1007/s001580130903z
[4] Paz, J., Díaz, J., Romera, L., Costas, M. (2014). Crushing analysis and multiobjective crashworthiness optimization of GFRP honeycombfilled energy absorption devices. Finite Elements in Analysis and Design, 91: 3039. https://doi.org/10.1016/j.finel.2014.07.006
[5] Meschut, G., Janzen, V., Olfermann, T. (2014). Innovative and highly productive joining technologies for multimaterial lightweight car body structures. Journal of Materials Engineering and Performance, 23(5): 15151523. https://doi.org/10.1007/s1166501409623
[6] Meschut, G., Matzke, M., Hoerhold, R., Olfermann, T. (2014). Hybrid technologies for joining ultrahighstrength boron steels with aluminum alloys for lightweight car body structures. Procedia Cirp, 23: 1923. https://doi.org/10.1016/j.procir.2014.10.089
[7] Irisarri, F.X., Lasseigne, A., Leroy, F.H., Le Riche, R. (2014). Optimal design of laminated composite structures with ply drops using stacking sequence tables. Composite Structures, 107: 559569. https://doi.org/10.1016/j.compstruct.2013.08.030
[8] Delogu, M., Zanchi, L., Dattilo, C.A., Pierini, M. (2017). Innovative composites and hybrid materials for electric vehicles lightweight design in a sustainability perspective. Materials Today Communications, 13: 192209. https://doi.org/10.1016/j.mtcomm.2017.09.012
[9] Akhshik, M., Panthapulakkal, S., Tjong, J., Sain, M. (2017). Life cycle assessment and cost analysis of hybrid fiberreinforced engine beauty cover in comparison with glass fiberreinforced counterpart. Environmental Impact Assessment Review, 65: 111117. https://doi.org/10.1016/j.eiar.2017.04.005
[10] Raugei, M., El Fakir, O., Wang, L., Lin, J., Morrey, D. (2014). Life cycle assessment of the potential environmental benefits of a novel hot forming process in automotive manufacturing. Journal of Cleaner Production, 83: 8086. https://doi.org/10.1016/j.jclepro.2014.07.037
[11] Sorenson, S., Ebbitt, G., Smith, S., Remtema, T. (2017). Optimizing transmission loss for lightweight body structures. In InterNoise and NoiseCon Congress and Conference Proceedings, 254(2): 204209. https://doi.org/10.4271/2017011812
[12] Mayyas, A., Omar, M., Hayajneh, M., Mayyas, A.R. (2017). Vehicle's lightweight design vs. electrification from life cycle assessment perspective. Journal of Cleaner Production, 167: 687701. https://doi.org/10.1016/j.jclepro.2017.08.145
[13] Lv, T.T., Wang, D.F., Wang, C.Q. (2018). Multiobjective lightweight optimization on closed BIW based on analysisdriven design. Automotive Engineering, 8: 912917. https://doi.org/10.19562/j.chinasae.qcgc.2018.08.007
[14] Wang, D.F., Cai, K.F., Ma, M.H., Zhang, S. (2018). Lightweight design of BIW based on implicit parametric model. Automotive Engineering, 40(5): 610616. https://doi.org/10.19562/j.chinasae.qcgc.2018.05.017
[15] Chabbouh, M., Bechikh, S., Hung, C.C., Said, L.B. (2019). Multiobjective evolution of oblique decision trees for imbalanced data binary classification. Swarm and Evolutionary Computation. https://doi.org/10.1016/j.swevo.2019.05.005
[16] Karka, P., Papadokonstantakis, S., Kokossis, A. (2019). Environmental impact assessment of biomass process chains at early design stages using decision trees. The International Journal of Life Cycle Assessment, 126. https://doi.org/10.1007/s11367019015910
[17] De Mello, R.F., Manapragada, C., Bifet, A. (2019). Measuring the shattering coefficient of decision tree models. Expert Systems with Applications, 137: 443452. https://doi.org/10.1016/j.eswa.2019.07.012
[18] Mu, Y., Wang, L., Liu, X. (2018). A fast rank mutual information based decision tree and its implementation via Map‐Reduce. Concurrency and Computation: Practice and Experience, 30(10): e4387. https://doi.org/10.1002/cpe.4387
[19] Joudi, N., Andrade, F., Llanes, I., Garcia, M.R., Kramer, D., Carugno, J. (2018). 101: Analysis of implementation of a hysterectomy clinical decision tree algorithm in a large academic center. American Journal of Obstetrics & Gynecology, 218(2): S953. https://doi.org/10.1016/j.ajog.2017.12.120
[20] Benkercha, R., Moulahoum, S. (2018). Fault detection and diagnosis based on C4. 5 decision tree algorithm for grid connected PV system. Solar Energy, 173: 610634. https://doi.org/10.1016/j.solener.2018.07.089
[21] Segatori, A., Marcelloni, F., Pedrycz, W. (2017). On distributed fuzzy decision trees for big data. IEEE Transactions on Fuzzy Systems, 26(1): 174192. https://doi.org/10.1109/TFUZZ.2016.2646746
[22] Akben, S.B. (2018). Predicting the success of wart treatment methods using decision tree based fuzzy informative images. Biocybernetics and Biomedical Engineering, 38(4): 819827. https://doi.org/10.1016/j.bbe.2018.06.007
[23] Khosravi, K., Pham, B.T., Chapi, K., Shirzadi, A., Shahabi, H., Revhaug, I., Bui, D.T. (2018). A comparative assessment of decision trees algorithms for flash flood susceptibility modeling at Haraz watershed, northern Iran. Science of the Total Environment, 627: 744755. https://doi.org/10.1016/j.scitotenv.2018.01.266
[24] Khedr, A.E., Idrees, A.M., El Seddawy, A.I. (2016). Enhancing Iterative Dichotomiser 3 algorithm for classification decision tree. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 6(2): 7079. https://doi.org/10.1002/widm.1177
[25] Cherfi, A., Nouira, K., Ferchichi, A. (2018). Very fast C4.5 decision tree algorithm. Applied Artificial Intelligence, 32(2): 119. https://doi.org/10.1080/08839514.2018.1447479
[26] Wang, D.M., Lu, C.H., Jiang, W.W., Xiao, B.R., Li, B.R. (2015). Study on PSObased decisiontree SVM multiclass classification method. Journal of Electronic Measurement and Instrument, (4): 611615. https://doi.org/10.13382/j.jemi.2015.04.018
[27] Han, M., Wang, Z.H., Ding, J. (2016). Efficient decision tree for evolving data streams based on frequent patterns. Chinese Journal of Computers, (8): 15411554. https://doi.org/10.11897/SP.J.1016.2016.01541
[28] Guo, Q., Zou, G. (2017). Prediction methods for extension architecture programming based on decision tree classification. CAAI Transactions on Intelligent Systems, 12(1): 117123. https://doi.org/10.11992/tis.201610015
[29] Wen, S., Li, W. (2014). Application of ontology knowledge expansion analysis tree in the extension strategy generation system. CAAI Transactions on Intelligent Systems, (1): 24. https://doi.org/10.3969/j.issn.16734785.201208037