Advanced Engineering Informatics 27 (2013) 386–394

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Advanced Engineering Informatics

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Product form design using customer perception evaluation by acombined superellipse fitting and ANN approach

1474-0346/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.aei.2013.03.006

⇑ Corresponding author.E-mail address: cy.tang@polyu.edu.hk (C.Y. Tang).

C.Y. Tang a,⇑, K.Y. Fung a, Eric W.M. Lee b, G.T.S. Ho a, Kin W.M. Siu c, W.L. Mou a

a Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kongb Department of Civil and Architectural Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kongc School of Design, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

a r t i c l e i n f o a b s t r a c t

Article history:Received 5 March 2012Received in revised form 3 September 2012Accepted 27 March 2013Available online 18 May 2013

Keywords:Affective designProduct aestheticsProduct formSuperellipse fittingArtificial neural network

Product aesthetics plays an important role in new product design and development. Product form candeliver product images and affect customer’s impression to a product. However, it is usually difficultto apply conventional approaches to represent the product form precisely and effectively for modelingthe relationship between product image and customer perception. The objective of this work is todevelop a computational technique for product aesthetics design so that customer perception can betaken into product form design in a more systematic and intelligent manner. To achieve this aim, a novelparametric approach is proposed to introduce design parameters such as line, size, and ratio into productdesign model and the technique of generalized superellipse fitting is adopted to describe the outline pat-tern of a product. Since customer perception on a product is highly non-linear and very difficult to bedescribed by any traditional mathematical approaches, an artificial neural network (ANN) model is there-fore established to relate the design parameters and the perceptual values for the design of a new prod-uct. A case study of mobile phone design, in which twelve numerical parameters are defined for theconceptual model, has been conducted to explain the implementation of the proposed approach. Athree-layered perceptron ANN model is developed to predict the perceptual values of stylishness basedon a survey using 32 mobile phone samples. The results of the case study illustrate that the proposedapproach can successfully generate an optimum design of a mobile phone by applying a genetic algo-rithm (GA) on the trained ANN model.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Product aesthetics and customer perception

Affective product design plays an important role to enhanceconsumers’ satisfaction for achieving a market success. Productaesthetics appeals to consumers, and evokes their psychologicalfeelings and perspectives to products [23]. Consumers often selecta product with aesthetic design that matches with their preference,especially when product alternatives are similar in terms of func-tions and price. In addition, product aesthetics influences custom-ers’ affective response, and eventually affects transactionalconsumer outcome [23].

Design process is usually relied on the designers’ talent, senseand experience in the industry. The design intention of a productis sometimes subjective for a project team to compromise anddecide a final design [36]. Besides, there are several gaps of cogni-tion between designers and customers [24,5]. In the other words, a

designer may not fully understand customer’s needs, or customersmay not realize his or her design intents because the art or designaccomplishments between the designer and his or her customersare different. Conjoint analysis and perceptual map are the conven-tional marketing techniques for designers to evaluate the prefer-ence of customers [26]. By comparing the product alternatives, itcan visualize the marketing positions of those alternatives. Never-theless, it is difficult to identify what are the significant designcharacteristics and what are their corresponding product imagesexpressing. A more systematic technique is desired for quantifyingand modeling the relationships between design characteristics andcustomer perceptual.

1.2. Product design and Kansei engineering

Kansei engineering has been proposed to deal with customers’psychological feelings regarding a product design [20,21]. A Kanseiengineering framework is mainly consisted of product images eval-uation and relational analyses of design characteristics and prod-uct images. Nagamachi [20] proposed a category classificationmethod to classify design elements into different product images

Fig. 1. Superellipses for different values of e.

C.Y. Tang et al. / Advanced Engineering Informatics 27 (2013) 386–394 387

through a top-down classification. Apart from the qualitativemethod, Nagamachi et al. [22] proposed a Kansei statistical analy-sis to quantify the effect of design elements to certain productimages of a product domain. This method mainly includes an eval-uation experiment to acquire customer perception on productsamples with regard to certain product images using semantic dif-ferential method, and statistical analyses of design relationshipusing principal component analysis and multiple regression analy-sis. Some previous research works have been employed the Kanseiengineering approach to study product aesthetics, for exampleexterior design of digital camera [2] and tactile sense of plasticproducts [4].

Traditional Kansei engineering approaches usually apply mor-phological analysis to decompose the design space of a productdomain into design elements in categorical items. For conceptualdesign, product form features are commonly defined in graphicalterms because it is simple and comprehensible for human users tounderstand complex shapes and patterns. For example, morpholog-ical analysis has been applied to handle the complicated productform of mobile phone design in previous research [16,18,32]. Themethod has been found to be useful for generating new design solu-tions by combining the modular items of different design elements.However, it is believed that these researches are slightly narroweddown to modularization as the optimal design outcome highlydepends on the options provided for selection. Moreover, the draw-back is unable to depict the geometries precisely because manydesign details are often lost during the process of discretization.

1.3. Parametric design

Geometry, topology, and shape morphing are some popularmethods used in the parametric design [1]. To design a cylindricalobject, Yanagisawa and Fukuda [38] proposed a curve model basedon varying distance and angle between nodes of a spline and theradius for revolving the spline. Shape morphing method has beenemployed to generate a transition shape between two differentshapes by varying a morphing ratio for product form generation[11]. Besides, an automatic design system for a door lock has beenproposed to generate a product form through controlling theparameters of a feature-based computer aided design (CAD) model[12,33]. Recently, Chen and Chang [3] has proposed a numericaldefinition-based systematic approach (NDSA) which employsnon-uniform rational basis spline (NURBS) curves and sectionalshapes for product form design of a kitchen knife.

In establishing a parametric CAD model, it is essential to definea curve. In the FIORES-II project, Podehl [28] has defined eight styl-ing terms for measuring the attributes of a curve, includingstraightness, sharpness, convexity, hollowness, crown, accelera-tion, tension, and lead-in. The eight styling terms can be denotedby a number of formulas to represent a curve with turning points.Besides, splines curve fitting possesses a greater flexibility to mod-el a curve in wide variety of shape [39]. However, splines fitting ob-tain x and y coordination of multiple knots that enlarge the datadimension significantly.

1.4. Computation model

Furthermore, the conventional approaches have the limitationsto explain the fuzziness and uncertainties of consumers’ feelingusing simple linear statistical models. To overcome this problem,computational intelligence techniques, such as artificial neuralnetworks (ANNs), have been applied recently for product aestheticdesign. ANN is a non-linear mapping mechanism, which is inspiredfrom the biological neural network of human being or creatures.The learning ability of ANNs is useful to model the non-linear rela-tionship between design characteristics and product images with

the use of survey data. There are several examples that ANN-basedapproaches are used for product aesthetics design, such as mobilephones [18], office chairs [11], and form-colour matching [19].

In the previous study [7], an ANN model is proposed to mapmobile design forms and customer perception. The customer af-fected knowledge is further extracted into rules showing howand which design elements influence in different semantic pairsas well. To enhance the coverage and contribution in product de-sign, form design should be extended to parametric approach, suchas dimensions, ratio, and curvature, for conceptual design on top offeature selection and module picking. This study is aimed to devel-op a computational method for product form design using artificialintelligence to evaluate product aesthetics and predict their influ-ence on customer perception regarding the visual impact of a prod-uct in a more objective and scientific way. Moreover, geneticalgorithm (GA) is also incorporated into the computational modelto determine the values of design parameters for the optimumproduct form [27].

This paper is organized as follows: Section 2 introduces the gen-eralized superellipse fitting for image quantification. Section 3 pro-vides the parameter setting for case study. The ANN modelconcerning customer perception and GA optimization in productform design are described in Sections 4 and 5 respectively. Section6 shows the results while Section 7 draws conclusion.

2. Superellipse fitting

2.1. Forms and superellipses

In product design, it is easy to observe the use of form primi-tives, such as circles, ellipses, squares and rectangles. The typicalway is to define the shapes in a list of categorical terms. To gener-ate the parametric model, a generic form is required to representthose primitives. A superellipse, which is an extension of an ellipse,can represent a large variety of shape, such as asteroids, circle,squircles, and rectangles [31]. Apart from this, Fuge et al. [6] sup-ported that superellipse is good enough to define the product out-line in various ways for conceptual design. The algebraic definitionof a superellipse can be expressed as

xa

��� ���2e þ yb

��� ���2e ¼ 1 ð1Þ

where x and y are the coordinates of points on the superellipse; aand b are the semi-diameters; and e is the parameter of squareness.

The shape of a superellipse can be varied significantly by adjust-ing the value of e, as shown in Fig. 1. The superellipses are flexibleto model various curve segments in a relatively simple expressionin comparison with the splines. Superellipses have been applied incomputer vision for shape detection [14], shape decomposition[13]. Osian et al. [25] proposed using affine superellipses (ASEs)to model contours, such as car windows and headlights in com-puter vision.

The same exponential power 2/e is usually applied to both thex and y directions for construction of a typical superellipse. It isunable to express the deformation under different bending ratein the x and y directions for some curve styles, such as lead-inand tension [28].

Fig. 2. Measurements on the curve of top shape of a phone.

388 C.Y. Tang et al. / Advanced Engineering Informatics 27 (2013) 386–394

To overcome this constraint, we propose fitting the curve seg-ments with the generalized superellipse. Based on Eq. (1), the gen-eralized superellipse is defined as

xa

��� ���2p þ yb

��� ���2q ¼ 1 ð2Þ

where p and q replace the parameter e in the orthogonal directions.A point (x,y) on the generalized superellipse can be expressed

as follows:

xðhÞ ¼ jcoshjp � asgnðcoshÞ ð3Þ

yðhÞ ¼ jsinhjq � bsgnðsinhÞ ð4Þ

Fig. 3. Body dimensions and layout parameters.

2.2. Generalized superellipse fitting

For a typical superellipse, e = p = q, it is very difficult to solve forh analytically [14]. To determine the value of e, the superellipse fit-ting uses the cost function and the gradient descent method to fitthe point data. The cost function can be defined by the ray of centremethod [31,13]. A line passing through the centre of the superel-lipse and the estimated point is used to calculate the radial dis-tance between an estimated point (xe,ye) and the intersect point(xi,yi) of the line and the superellipse. The distance can be calcu-lated by

d ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxi � xeÞ2 þ ðyi � yeÞ

2q

xe ¼1a

� �2e

þ yi

xi� 1

b

� �2e

����������e2

ye ¼ xeyi

xi

� �ð5Þ

However, it may not be possible to derive a formula, like Eq. (5), fordetermining xe for the generalized superellipse where p – q. To findp and q for the generalized superellipse, the problem can be solvedby fitting the points with the least-square method. Based on Eq. (2),the theoretical y-coordinate of the generalized superellipse can becalculated by,

y0i ¼ �b

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� j xi

aj

2p

2q

rð6Þ

Hence, the objective function is to minimize the sum of squareerrors

SSE ¼Xn

i¼1

ðjy01j � jyijÞ2 ð7Þ

3. Setting design parameters

A case study of mobile phone design is carried out to reveal thedetails in product form design using the proposed approach. Toconduct product form design computationally, design parametersmust be defined in a way that they can be adequately describedthe product form. Design parameters in four major classes involving

Fig. 4. Parameters of navigating button (a) r

body dimensions, contour, layout, and shape of components are de-fined to describe the common feature of mobile phones.

The contour of a mobile phone is considered as a combination oftwo curve segments: one is the top shape and another is the bot-tom shape. Based on the observation, there are mainly three kindsof the shape, namely, (1) shape corner, (2) filleted corner, and (3)full curvature. The conjunction of the curve and side edge impli-cates a horizontal baseline, which divides the curved region fromthe body. Five points, P0, P1, P2, P3, and P4, are taken on half sideof the curve as shown in Fig. 2. The values of a and b are set equalto half of the phone width and the maximum deviation from thebaseline of curve, respectively. The values of p and q are then ob-tained using the generalized superellipse fitting by the least squaremethod as described in Section 2.2.

For the form of a mobile phone, overall dimensions, such aslength (L), width (W), and thickness (T), are taken as the basic de-sign parameters as shown in Fig. 3. Other design parameters repre-senting the relative size of the screen and keypad of a mobilephone are the upper space (St), the length of screen (Sl), and thelower space (Sb). For the length width ratio of the screen, as mostof the models provided in current market is 4:3, and therefore, itis set as default value in this experiment and is absent from com-putation model. In addition, the width of border/frame (B) is alsochosen as a design parameter. In this case study, the size (l) andshape (Bs) of a navigating button are considered as the commoncharacteristics in the form design of mobile phones. The buttonshape (Bs) is classified as ‘0’ for round and ‘1’ for square-like

ectangular type, and (b) circular type.

Fig. 6. Chromosome encoding.

Table 2Results of superellipse fitting for the bottom shape.

Sampleno.

1 2 3 4 5 6 7 8

Bottom shapea 24.45 23.95 25.82 23.06 22.01 27.07 24.29 23.63b 7.71 7.71 21.95 13.79 10.77 8.16 7.35 5.51p 0.64 0.47 0.58 0.60 0.56 0.31 0.18 0.13q 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00RMSE 0.32 0.68 0.39 0.83 0.38 0.23 0.87 0.66

Sampleno.

9 10 11 12 13 14 15 16

Bottom shapea 25.08 25.94 26.98 26.53 24.05 27.12 26.69 26.03b 26.18 10.11 5.28 5.28 8.98 3.09 9.44 6.22p 0.26 0.54 1.00 1.00 0.48 0.34 0.34 0.29q 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00RMSE 1.77 0.42 0.49 0.55 0.59 0.09 0.27 0.09

Sampleno.

17 18 19 20 21 22 23 24

Bottom shapea 27.61 22.75 22.75 22.64 23.09 24.94 23.76 21.60b 8.03 5.55 8.98 5.08 5.07 15.86 4.54 8.95p 0.31 1.00 0.40 0.32 1.00 0.55 0.24 0.38q 1.00 1.00 1.00 1.00 0.70 0.83 1.00 1.00RMSE 0.25 0.39 0.26 0.12 0.43 0.26 0.34 0.36

Sampleno.

25 26 27 28 29 30 31 32

Bottom shapea 23.96 23.61 23.41 28.54 26.89 27.39 27.39 25.68b 7.66 10.20 5.10 10.45 12.21 8.68 10.43 6.70p 0.31 0.44 0.15 0.24 0.40 0.68 0.32 0.26q 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00RMSE 0.43 0.30 0.33 0.12 0.24 0.04 0.35 0.47

Fig. 5. ANN for modeling product form and perception.

Table 1Results of superellipse fitting for the top shape.

Sampleno.

1 2 3 4 5 6 7 8

Top shapea 24.45 23.95 25.82 23.06 22.01 27.07 24.29 23.63b 9.40 6.22 18.70 8.98 6.12 8.77 6.52 1.70p 0.64 0.47 0.72 0.75 0.50 0.40 0.18 0.13q 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00RMSE 0.39 0.55 0.73 0.34 0.31 0.45 0.77 0.20

Sampleno.

9 10 11 12 13 14 15 16

Top shapea 25.08 25.94 26.98 26.53 24.05 27.12 26.69 26.03b 5.94 7.26 4.66 2.26 7.45 5.42 8.43 2.01p 0.33 0.87 1.00 0.97 0.48 0.34 0.34 0.31q 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00RMSE 0.19 0.16 0.15 0.02 0.49 0.15 0.24 0.12

Sampleno.

17 18 19 20 21 22 23 24

Top shapea 27.61 22.75 22.75 22.64 23.09 24.94 23.76 21.60b 7.53 3.17 8.40 3.15 4.72 8.47 4.09 8.24p 0.31 1.00 0.40 0.32 1.00 0.39 0.24 0.39q 1.00 1.00 1.00 1.00 0.70 1.00 1.00 1.00RMSE 0.23 0.15 0.25 0.07 0.40 0.21 0.30 0.31

Sampleno.

25 26 27 28 29 30 31 32

Top shapea 23.96 23.61 23.41 28.54 26.89 27.39 27.39 25.68b 5.55 3.86 2.64 9.61 9.61 7.26 8.75 3.80p 0.31 0.24 0.15 0.24 0.40 0.68 0.32 0.26q 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00RMSE 0.31 0.33 0.17 0.11 0.19 0.03 0.29 0.26

C.Y. Tang et al. / Advanced Engineering Informatics 27 (2013) 386–394 389

(Fig. 4). Moreover, the ratio l/Sb is used as a constraint parameter toavoid oversizing of the button.

Stylishness, one of the commonly used aesthetics’ wordings inmobile devices [17,37], being employed in the study is the measureof the customer perception on the mobile phone samples. The pairof perceptual wording comprises smart and clumsy (S–C) is used toelicit consumer’s perceptual stylishness value of each sample and

overall ratings are used to find the turning of described attributesgiving stylish impression to the majority.

4. Modeling product form and customer perception by ANN

ANNs have been used for solving specific problems such asregression, pattern recognition and data classification through alearning process by adjusting the values of the weights of connec-tions among the neurons. Multilayered perceptron (MLP) [30] isthe most widely adopted ANN model in different industries. In par-allel, back-propagation (BP) is the most popular supervised learn-ing method for training MLP model. Lai et al. [18,19] havestudied MLP for traditional parametric approach and morphologi-cal approach in product aesthetic. Likewise, a typical three-layeredBP network, which consists of an input layer, a hidden layer and anoutput layer of neurons, is applied in this study for form-aestheticsmodeling and testing the proposed ratio-based parametric ap-proach. The architecture of the MLP model is illustrated in Fig. 5.

Table 3Measured values of the design parameters and the perception of stylishness.

No. Top-p Top-b Btm-p Btm-b St Sl Sb W T B l/Sb Bs ||S–C||

1 0.64 9.40 0.64 7.71 10.5 40.8 49.1 48.9 14.1 2.14 0.34 1 0.3822 0.47 6.22 0.47 7.71 11.5 36.9 53.1 47.9 13.7 2.30 0.14 1 0.5273 0.72 18.70 0.58 21.95 14.7 25.3 49.1 51.6 23.0 3.30 0.50 0 0.8554 0.75 8.98 0.60 13.79 18.7 23.9 44.8 46.1 14.4 3.20 0.46 0 0.4005 0.50 6.12 0.56 10.77 16.9 24.4 29.6 44.0 12.9 5.70 0.46 1 0.3276 0.40 8.77 0.31 8.16 12.7 49.5 32.8 54.1 18.1 1.77 0.44 1 0.7647 0.18 6.52 0.18 7.35 15.5 50.5 37.6 48.6 18.7 0.92 0.45 1 0.7648 0.13 1.70 0.13 5.51 12.2 49.8 32.5 47.3 13.5 1.03 0.47 0 0.4739 0.33 5.94 0.26 26.18 14.6 22.3 49.0 50.2 17.5 3.96 0.38 0 0.727

10 0.87 7.26 0.54 10.11 16.9 18.5 68.1 51.9 8.8 1.35 0.31 0 0.12711 1.00 4.66 1.00 5.28 15.1 50.8 42.3 54.0 21.3 4.46 0.35 1 0.76412 0.97 2.26 1.00 5.28 10.9 51.8 35.8 53.1 20.9 4.01 0.46 1 0.89113 0.48 7.45 0.48 8.98 17.9 32.7 37.9 48.1 15.2 4.16 0.41 1 0.47314 0.34 5.42 0.34 3.09 17.6 57.7 24.1 54.2 11.1 2.12 0.35 1 0.00015 0.34 8.43 0.34 9.44 19.1 46.1 35.7 53.4 17.8 1.80 0.54 0 0.70916 0.31 2.01 0.29 6.22 17.9 58.7 26.9 52.1 16.6 2.23 0.46 1 0.61817 0.31 7.53 0.31 8.03 17.9 58.0 23.4 55.2 16.6 3.23 0.37 1 0.67318 1.00 3.17 1.00 5.55 14.9 35.2 54.2 45.5 10.6 3.17 0.28 1 0.40019 0.40 8.40 0.40 8.98 12.0 40.1 51.3 45.5 16.6 1.43 0.24 1 0.67320 0.32 3.15 0.32 5.08 11.4 37.4 54.3 45.3 13.1 2.50 0.24 1 0.69121 1.00 4.72 1.00 5.07 15.2 29.9 59.4 46.2 15.6 1.28 0.31 0 0.72722 0.39 8.47 0.55 15.86 12.1 36.8 55.5 49.9 12.9 1.76 0.28 0 0.63623 0.24 4.09 0.24 4.54 14.8 42.6 44.0 47.5 17.2 2.08 0.30 1 1.00024 0.39 8.24 0.38 8.95 18.4 29.0 50.3 43.2 11.2 1.59 0.28 1 0.41825 0.31 5.55 0.31 7.66 15.0 37.0 39.6 47.9 15.8 1.98 0.39 0 0.70926 0.24 3.86 0.44 10.20 24.4 29.8 40.3 47.2 19.3 3.32 0.57 0 0.85527 0.15 2.64 0.15 5.10 15.4 41.6 37.3 46.8 13.3 1.59 0.46 0 0.60028 0.24 9.61 0.24 10.45 19.4 62.7 17.3 57.1 11.4 2.80 0.63 0 0.36429 0.40 9.61 0.40 12.21 11.3 43.2 33.1 53.8 9.8 3.30 0.52 0 0.38230 0.68 7.26 0.68 8.68 12.1 45.4 46.0 54.8 14.2 3.76 0.33 1 0.67331 0.32 8.75 0.32 10.43 12.1 47.2 47.8 54.8 16.5 4.64 0.34 1 0.76432 0.26 3.80 0.26 6.70 10.0 50.6 34.6 51.4 19.1 1.11 0.45 0 0.964

Table 4Parameters of the ANN model.

Model parameters Value adopted

No. of attributes 12No. of input nodes 12No. of output nodes 1No. of hidden neurons 2

3 ð12þ 1Þ ¼ 8:67 � 9Activation function Log-sigmoid functionTraining function Levenberg–Marquardt backpropagationNo. of stall epochs 10,000

390 C.Y. Tang et al. / Advanced Engineering Informatics 27 (2013) 386–394

For the parametric approach, the network has N input nodes,where N is equal to the number of design parameters. The ANN isfed with an input vector, which contains values of those designparameters of a design instance. A single output node responses totrigger a perceptual value of the corresponding input parametersthrough sigmoid function. Although ANN can support multiple out-puts, a single output model usually gives a faster and better perfor-mance of data learning than a multiple-output model. The MLPmodel has been proven to be a universal function approximator[10] subject to the provision of sufficient number of hidden neurons.However, there is no analytical approach to determine the requirednumber of hidden neurons prior to the network training. In fact, ifthe one knows nothing about a system including its non-linearitybehavior, logically, it is not possible to determine the required num-ber of hidden neurons. However, there are several rule-of-thumbsdeveloped for rough estimation. The rule of thumb adopted in thisstudy is the one developed by Heaton [9]. The recommended num-ber of the hidden neurons can be obtained by Eq. (8) as follows:

Hn ¼23ðIn þ OnÞ ð8Þ

where Hn, In, and On are respectively the number of hidden neurons,the input neurons, and the output neurons in the MLP model.

5. Optimizing design parameters by GA

To search for the global solution, GA is proposed to function onthe trained neural network mapping design and perceptual values.Its randomness nature brings benefits in getting away from localoptima and overfitting reported on ANN [15,8] and searching con-figuration solution of design parameters sit on inputs of trainedneural network. The input nodes of network are encoded into chro-mosome in terms of real number and binary coding with respect totheir nature. Fig. 6 shows the encoding system of the chromosomeused in the algorithm. Basically, the all predefined design parame-ters are divided into two categories, real number and binary num-ber, and located as shown. Each real node gene carries the actualmeasure of its representing design parameter while binary genecould be used for making selection among two variables, i.e. squareor round button, or showing a feature is enabled or not, i.e.Bluetooth.

The initial population is created for C chromosomes with ran-dom number within allowable range of each gene. The fitness func-tion, output node of neural network, is used to evaluate theperformance of chromosomes and is shown in Eqs. (9) and (10) [7].

wk ¼ f1ðW 0jk f 1ðWijXm þ bjÞ þ b0kÞ ð9Þ

wk ¼2

1þ e

�2XJ

j¼1

W 0 jk 2

1þe

�2

XI

i¼1

ðxi�Wijþbj Þ

" #�1

0BBBB@

1CCCCAþb0k

2666664

3777775

� 1 ð10Þ

where wk is the output of ANN, ft(s) is the tan-sigmoid transfer func-tion, Wij is the weight linking ith input node and jth hidden node,W 0

jk is the weight linking jth hidden node and kth output node, Xm

Fig. 7. Graph of superellipse fitting for top shape of samples 1 and 2.

NUMBER OF HIDDEN NEURONS

ASO

LUTE

ER

RO

R ,|

e|

4 6 8 10 12 140

2

4

6

Fig. 8. Sensitivity analysis of optimal hidden neurons.

C.Y. Tang et al. / Advanced Engineering Informatics 27 (2013) 386–394 391

is the input vector, bj and b0k are biases of hidden and output nodesrespectively.

Chromosomes are then undergone Roulette-Wheel selection,reproduction using crossover and mutation to search for optimal

solution, parent replacement by outstanding offspring, and reiter-ation of these processes until the predefined generation numberacts as stoppage criteria is reached [27]. Lastly the chromosomeperforming the best in fitness function, a maximum or minimumaccording to the objective, is extracted and decoded into designparameters mentioned before.

6. Results

6.1. Superellipse fitting for the body shape

A survey on mobile phone design was conducted to acquire theperception values regarding the stylishness of 32 mobile phonesamples as shown in Appendix. The respondents were asked to ratea 5-point Likert scale (of which ‘1’ represents smart, and ‘5’ repre-sents clumsy) for each greyscale photo with both front view andside view of a mobile phone sample. The results of superellipse fit-ting for the top and bottom shapes are listed in Tables 1 and 2,respectively. To illustrate the coordinate data obtained, Fig. 7 isused to show the graphical results of sample 1 and 2, with crosspoints and respective superellipse fitting for the top shape ob-tained by minimizing the sum of square error of coordinates.According to the results, most of the values of parameter q areequal to one except sample 21 and 22. Therefore, the parameterq is removed from the list of the attributes. Besides, the parametera is duplicated with the width, so only the parameter W is includedin the attribute list. A smaller value of p represents the curve has ahigh tension at the corner, such that a sharper corner is resulted.Table 3 shows superellipse fitting value, p, b of top and bottomshape, the parameter values defined in Section 3 and the normal-ized perceptual values of ‘‘smart–clumsy’’, ||S–C||, where smart atthe lowest extreme while clumsy at another one, for the 32 mobilephone samples.

6.2. ANN Model and Leave-one-out Validation

Based on Eq. (8), the number of hidden nodes was calculated.The layer sizes of the ANN are summarized in Table 4. By therule-of-thumb, the number of hidden neurons was determined tobe 9. Prior to the adoption, a sensitivity study was carried out tocheck whether the rule-of-thumb employed is consistent withthe analytical result by repeating the training and testing proce-dures with a range of hidden neurons. To test the performance ofthe model in this study, networks with different number of hiddenneurons varying from 4 to 14 (i.e. 9 ± 5) are chosen for making acomparison. For each number of hidden neuron, 100 trials wereperformed. A log-normal distribution was fitted to the 100 pre-dicted errors since the error is ranged between 0 and1. The upperand lower limits of the central 95% confidence interval were plot-ted as error bar. Fig. 8 shows that the error bars of the models withdifferent number of hidden neurons overlap with each other. Thissensitivity study might conclude that the performance of the mod-el is insensitive to the number of hidden neurons and the rule-of-thumb works appropriately in this case.

Leave-one-out validation is adopted to evaluate the perfor-mance of the trained MLP model. Among the total 32 samples,one sample was held out for the evaluation of testing error. Theother 31 samples were randomly divided into the training setand the validation set with the respective percentages as 80%and 20%. In the course of network training, early-stop trainingwas adopted. In each training epoch, the training error and valida-tion error were obtained. The training error was used by BP to ad-just the weights of the MLP model while the validation error wasused for stopping the training process if the validation error inthe course of model training had no further reduction over a prede-

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

FOLD

AB

SOLU

TE E

RR

OR

, |e|

Fig. 9. Absolute errors, |e|, of ANN model (leave-one-out validation).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

90% Confidence Limit = 0.33

p(|e

|)

ABSOLUTE ERROR, |e|

Fig. 10. Beta distribution of absolute error, |e|, for ANN model.

14.149.1 48.940.80.64 10.57.710.649.40 10.342.14

Top-p BTWSbSlStBtm-bBtm-pTop-b Bsl/Sb

Real Nodes Binary Nodes

Fig. 11. A sample chromosome.

Table 5Close-optimal parameters generated by the GA optimization on the trained ANNmodel.

Top-pa

Top-bb

Btm-pc

Btm-bd

St Sl Sb W T B l/Sb Bs

0.13 18.70 0.13 26.18 24.4 62.7 27.0 52.6 8.8 0.90 0.50 0

a Squareness of x-coordinate points on the generalized superellipse of the topshape.

b The maximum deviation from the baseline of curve of the top shape.c Squareness of x-coordinate points on the generalized superellipse of the bottom

shape.d The maximum deviation from the baseline of curve of the bottom shape.

Fig. 12. Illustration of the optimal mobile phone design.

392 C.Y. Tang et al. / Advanced Engineering Informatics 27 (2013) 386–394

termined number of epochs which was chosen to be 1000 after fewtrials. Upon the completion of model training, the MLP model wasapplied to the held-out sample to evaluate prediction error in formof absolute error, |e|. The above evaluation process was repeatedagain with another sample being held out. Eventually, a total of32 predicted errors were obtained as shown in Fig. 9.

Beta distribution was adopted to fit the 32 prediction errors asshown in Fig. 10. It showed that the 90% one-sided confident limit

was determined to be 0.33. It implied that, with 90% confidence le-vel, the prediction error should not be higher than 0.33. In thisstudy, a particularly low prediction error was not expected. Sincethe responses of the questionnaires vary due to age, gender, educa-tion, experiences, etc. of the interviewees, certain degree of varia-tion was expected.

6.3. Optimization by GA

According to the ANN results, GA was applied to find the opti-mal values of the design parameters for the mobile phone form de-sign. To find a smart design, the objective function of GA wasdefined to find the parameters that could minimize the output ofthe ANN model, i.e. the value of ||S–C||. An initialized chromosomeusing data of sample 1 is used to illustrate the coding system forthis experiment as shown in Fig. 11. With reference to Section 3,almost all genes here are real numbered with the only exceptionalcase of button shape (Bs) for round and square selection. The opti-mization was performed with population size of 50, 90% crossoverand 10% mutation for 200 generations.

The close-optimal set of design parameters obtained by usingthe GA optimization is shown in Table 5. Moreover, the close-opti-mal product form is illustrated using an automatic builder asshown in Fig. 12. The optimal design has approximately the sameupper spacing and lower spacing. Hence, the screen is almost cen-tre-aligned. As the screen occupies a large proportion, it leads todesign the layout without a keypad, but navigating button onlyin the lower space. Besides, the optimal dimensions with lengthwidth ratio around 2.17:1 and slim 9 mm design makes it looks talland neat. In the component level, the optimal design contains anarrow border, a big screen and a round button. The resulted illus-tration is just a template, which depicts the conceptual design

Fig. A.1. Mobile samples used for conducting customer perception.

C.Y. Tang et al. / Advanced Engineering Informatics 27 (2013) 386–394 393

based on the defined parameters only. In real life practice, design-ers can base on this conceptual design to achieve the final product

design by introducing further details or functions, such as surfacefinish and video camera.

394 C.Y. Tang et al. / Advanced Engineering Informatics 27 (2013) 386–394

7. Conclusions

In this study, a novel parametric approach has been developedfor product form design using the generalized superellipse fittingand ANN. A case study of mobile phone design was conducted toexplain the implementation of the proposed approach for produc-ing an optimal form design. In the case study, a three-layer MLPwas used to map design parameters and the perceptual value ofstylishness based on a survey using 32 mobile phone samples. Byapplying GA, the output of the trained MLP model was minimizedto give the values of design parameters for the near-optimal solu-tion of a smart mobile phone design.

The results support the integration of ANN and GA into an intel-ligent design approach for mobile phone design and optimizationwith participation of customer perception. With the use of general-ized superellipse fitting, various product images or design formsare generalized and quantified in a precise expression leading datamining into design aided field. The setting of the ANN and GA usedin this research lie within widely accepted standard, however, anexclusive study in performance of different forms of network andevolutionary algorithm would be interesting. A comprehensivestudy with multiple design outputs might bring unexpected contri-bution in understanding customer needs to a further extent. Be-sides, the definition of superellipse could be further extend to amore complex product design by using some advanced curve fit-ting methods, such as consecutive superellipses [35], 3D superel-lipse–superquadrics [29], or curvature integration and multi-resolution [34], etc. Moreover, it is believed that the proposedmethodology could be further investigated into other product de-sign industries with additional data mining techniques for a uni-versal decision support system.

Acknowledgements

The authors would like to thank the Research Committee of theHong Kong Polytechnic University for their substantial support inthis study (Project Code: G-YJ10).

Appendix A

Fig. A.1.

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