Advanced Materials Research Vols. 118-120 (2010) pp 748-752 Online available since 2010/Jun/30 at www.scientific.net © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.118-120.748
A Quantitative Method on Formative Elements Optimization of Car Styling Design Li Zhuo 1, a, Xia Jinjun 2,b 1
School of Automotive Engineering, Wuhan University of Technology, Wuhan, China 2
College of Arts, Chongqing University, Chongqing, China a
[email protected], b
[email protected]
Keywords: BP neural network, Kansei Engineering, Formative element, Quantization
Abstract. According to the basic principles of Kansei Engineering and BP neural network, the article establishes a non-linear relationship between the user’s perceptual evaluation and the car’s formative element. It also builds a strong anti-interference black box model, which may work out the precise value of the formative elements by the perceptual evaluations. The paper also discusses the model with deductive method, and the results show that the quantization and transformation in body design can be effectively solved by the method based on BP neural network and Kansei Engineering. Introduction Kansei Engineering is a kind of design method which studies emotional feeling by using of rational methods. It quantifies the perceptual description for products and explores the relationship between psychological intention and design elements, in order to find a foundation and reference for design [1]. The questionnaire may express the user's emotional experience and estimate the tendency of design, but it is not enough. It is necessary for us to figure out the scope of the tendency, the precise value. Therefore, we need a quantitative approach to study the numeric values of formative elements in the design process[2]. Back Propagation Neural Network is a kind of one-way transmission and multi-layer feed forward neural network. It can be combined with the Kansei Engineering to obtain the desired results [3] . As the neural network is able to build a model directly when input and output data, and it has a strong non-linear mapping capability, the paper uses BP neural network modeling method to optimize the construction and reliability of the car’s body design forecasting models. Model Theory and Experiment In order to quantitatively describe the car’s body styling, we must establish the coordinates of the body shape, then take the coordinates of each sample as independent variables and select the subjects of the perceptual average evaluation of the sample as the dependent variables to carry out the training analysis of neural network. Finally, all variables training program should be standardized, so that we could calculate the quantized relationship between the perceptual evaluation and the formative elements. Based on the mapping, when enter the ideal evaluation and reverse to calculate each coordinate’s position, the shape matching to the kansei evaluation comes into being. Experimental preparation Get the side view of the sample car and identify several critical control points on the outline. For convenience the research, just taking the region from the fog lights to the windscreen to build the coordinate system, which the origin point (0,0) is located in the intersection of the horizontal line of the chassis and the vertical axis of the front wheel, as shown in Fig.1. In this way, the region of 10 control points P1 ~ P10 could be found at the coordinates of the corresponding location respectively, with Pi( x2i-1, x2i) to indicate that the P1( x1, x 2) , P2( x3, x 4) ... ... P10( x19, x 20) ; their coordinates are shown in Table 1.
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Fig.1 The graph of the body coordinates system Table 1 Coordinates of the 40 samples x1
x2
x3
x4
Sample 01
-19.56
1.5
-19.66
3
Sample 02
…
-16.3
…
1
…
-17.7
…
2.68
Sample 40
-21.2
0.74
-21.24
1.44
…
… … … … …
… … … … …
x17
x18
x19
x20
32
30
35.54
30.8
25.53
…
27.67
…
32.4
…
29.57
42.2
28.35
45.2
29.25
…
From the above table, the absolute value difference is too large to keep the balance of the whole situation, so it is better to take a normalized work, that is, all the data needs to be filtered into the secondary data between [0,1] by using the following formula: ∧
x=
x − x min x max − x min
In the formula, xmax indicates maximum sample data, x min means the minimum one [4]. The normalized data is omitted here. Conduct the normalized data as an input parameter and 4 evaluation semantics from questionnaires as an output parameter, the car’s body shape prediction model is build by the linked relationship between the input and output. Drawing 8 groups (numbered 5th, 10th, 15th, 20th, 25th, 30th, 35th, and 40th) from 40 groups as the test samples, the remaining 32 are used as network training data. Taking use of MATLAB neural network toolbox to setup training parameter, the target output is set to meet the precision value. By the end of simulation and testing, the error region is controlled in [-0.1, 0.1] between predicted and the original value, which means the model is relatively accurate. The inverse-model’s Construction and Training The above experimental preparation is carried out in the case of taking coordinates as independent variables and evaluation as the dependent variables. However, when the users’ experience need to be used to make sure the features of car’s design, the term becomes an inverse one, the model also becomes an inverse model. In order to get the precise coordinates of formative elements, assuming that other parts of the body segments are identified, we only discuss what the windshield form should be like in a given evaluation. Thus, taking 4 given semantic evaluation by the users and 20 known amount of inputs(from x1 to x16) as the independent variables [5], and using the two points (4 coordinates) in the end of windshield as the dependent variable, so the inverse model for car’s body prediction based on BP Neural Network is established. According to the neurons training results and scientific experience, structure 20-12-28-4 turns to be more rational, that means 20 input variables, 4 output variables, the number of neurons in first and second hidden layer are 35 and 18. The transfer function respectively is tansig, logsig and purelin[6]. The network structure is shown in Fig.2.
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Fig.2 The inverse model’s structure of the car’s body shape
Fig.3
The error curve of training in inverse model network
Run BP neural network in the MATLAB toolbox. Training the 32 groups data in Table 1 and setting up the largest step number as 8000 times, MSE error as 0.1. After 2376 times training, network training error is 0.103528, basically meet the requirements (the default error 0.1), as shown in Fig.3. After the simulation training network convergence, the error is mostly controlled in [-0.1, 0.1], which means the network model of training is successful. And then enter the 32 teams data to test, some of the results (due to the limited space, here lists only the first 6 groups) are shown as Table 2. Since the error’s plus or minus is no more than 0.2, it is obviously that the inverse model prediction operation is effective by using the inverse model to control the key points of the body shape. Table 2 Training and test results NO.
X17
X18
X19
X20
X17
X18
X19
X20
PREDICTION
PREDICTION
PREDICTION
PREDICTION
1
0.58704
0.70482
0.76967
0.44348
0.6385
0.7494
0.7433
0.4460
2
0.3251
0.56446
0.6948
0.33652
0.3314
0.5258
0.6873
0.3312
3
0.34413
0.40361
0.59704
0
0.3146
0.4309
0.5998
0.0219
4
0.5749
0.54819
0.78779
0.24348
0.5437
0.5446
0.6980
0.2433
5
0.2915
0.64458
0.60658
0.57652
0.2856
0.6334
0.5792
0.5581
6
0.40891
0.54217
0.70672
0.3
0.4618
0.5516
0.7383
0.2741
Testing the 8 groups while Network training is completed, then getting the results as Table 3: Table 3 Simulation and test results NO.
X17
X18
X19
X20
X17
X18
X19
PREDICTIO
PREDICTIO
PREDICTIO
N
N
N
X20 PREDICTION
1
0.4749
0.6506
0.7289
0.44348
0.4831
0.6547
0.7304
0.4428
2
0.38462
0.70482
0.66142
0.50435
0.3852
0.6995
0.6584
0.5106
3
0.12348
0.76627
0.55317
0.61739
0.1240
0.7767
0.5521
0.6140
4
0.51093
0.69157
0.74845
0.49391
0.5009
0.6921
0.7443
0.5148
5
0.32834
0.6506
0.6247
0.44696
0.3269
0.6487
0.6301
0.4465
6
0.26316
0.66325
0.61445
0.43913
0.2646
0.6631
0.6122
0.4383
7
0.41741
0.65422
0.72055
0.47739
0.40922
0.6529
0.7085
0.4832
8
1
0.60542
1
0.3087
0.9677
0.6118
0.9520
0.3115
Randomly drawing the seventh sample (numbered NO.35) from the whole 8 validation samples, anti-normalized the 4 predictive value to get the 2 points’ coordinates those are [27.8043, 29.1498], [33.4811, 31.1847]. Compared with the original data in Table 1, only a small error is discovered.
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So, the key points of the curve to control the shape are confirmed after anti-normalizing all of the data to restore the coordinates. The more enough key points being setup, the curve will be more smooth, and the target shape is more clear. Analysis and discussion Based on BP neural network, a body shape formative element of the solution model is established, designers can precisely control any segment in this model only by changing the input values according to the actual situation in specific application. For example, an investigation discovers that users prefer such a model: weighing coefficient of sport style is 0.6, lively sense 0.45, futuristic sense 0.3, mellow style 0.65. Then designers may input these evaluation values and basic segments of the coordinate into the BP network inverse-model to deduce the precise location of critical points on target region. The core idea in conversion is "clarify user’s preference→ convert to BP model parameter→ get the normalization value of prediction→ revert to the original coordinates." The quantitative solution method is an important complement to designer kansei feeling. Here is another inference based on the above cases: The design goal is to predict the sample 7 (No. 35 of samples) windshield curve shape. Market research shows people’s expectation are sport style is 60%, lively sense 45%, futuristic sense 30%, mellow style 65%. Input independent variables such as f1, f2, f3, f4 and the known key points in other regions into the inverse model, then the dependent variable, Windshield of the two control points (4 values) are outputted. The data is shown as follows in Table 4. Table 4 The data conversion between experimental evaluation value and the predictive value in the inverse BP model conversion of evaluation value Perceptual Percentage
conversion of Prediction value
,
normalization
[-3 3] Interval
Original coordinates
f1
60 %
1.80
x17
0.4132
27.7968
f2
45 %
1.35
x18
0.6255
29.0072
f3
30 %
0.90
x19
0.7833
33.4283
f4
65 %
1.95
x20
0.5029
30.7526
Fig.4 The restored map of the inverse model Based on the definition of the above table, points P9 and P10 could be tracked in the coordinates system, so the displacement contours of the Windshield trend and the specific location is clear controlled by these two points. Details are shown in Fig.4. The black line is the original patterns and the red one is for the prediction. In this way, entering a known ideal target (the user's evaluation) could gain the design details (each key points for control segments).Theoretically, as long as perfecting the training of BP neural network model and obtaining correspondence between
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input-output model, the more definition points are pointed, the more accurate the resulting line will be. Eventually, a smooth curve will be connected together. This is the quantitative method which calculate their match points (lines, angles) according to different levels of evaluation values. In actual design work, designers still have to pay attention to kansei feeling or intuitive. It is completely wrong to rigidly using above quantitative method to put all the works to the BP neural network or mathematical calculations. The quantitative method through the program operations is more suitable for the small region to choose the preciser one, as a strong support to the perceptual judgments and quantitative location. Conclusion Through experiments, the paper establishes the model based on BP neural network to study the issues on kansei engineering in car’s body design. It is effectively support or complement the design result. Theoretical analysis and experimental results both show that: (1) The study of introducing BP neural network to Kansei Engineering establish the nonlinear relationship between User’s perceptual evaluation and the formative elements. (2) Taking the perceptual evaluation and the other information as input, we could find out the coordinates of the corresponding form under the training of the network, and complete the quantization process. (3) establishing an appropriate correlation is much necessary in the design black box, precisely because of its strong anti-interference. It is particularly suitable for Kansei Engineering analysis. Although the solution is not the unique one, it is an optimal one. Experimental results show that the method is effective. References [1] Nagamachi: Kansei Engineering as A Powerful Consumer-oriented Technology for Product Development, Applied Ergonomics, Vol.33(2002), p.289 [2] Sato T, Hagiwara M. IDSET: Interactive Design System using Evolutionary Techniques, Computer-Aided-Design, Vol.33 (2001), p. 367 [3] G.Casalino, FM emola Capece Mitnttolo: A model for evaluation of lase welding efficiency and quality using an artificial neural network and fuzzy logic, edited by Engineering Manafacture, (2004), p.641 [4] Japan Institute of Urban Planning. Investigation and analysis of urban planning, Tokoyo Kashima Press (1990) . [5] M.Qiu, Semantic Similarity Measure and its Application in the Design Management System Applications, PhD thesis, Zhejiang University, (2006). [6] Y.Gong, 'eural 'etwork in Solving the Machining Error of Re-mapping Study of the Problem, Jilin University (2005).
Materials and Product Technologies II doi:10.4028/www.scientific.net/AMR.118-120 A Quantitative Method on Formative Elements Optimization of Car Styling Design doi:10.4028/www.scientific.net/AMR.118-120.748