# An Automated Design Method for Plane Trusses Based on User Preference Information
## 3 User Preference Prediction Model
### Identification of Truss Features  
Visual discrimination is the basis of expressing user preference for truss shapes. Hence, the selected features are required to reflect the geometric characteristics of truss shapes clearly. Then, the users can visually discern the difference between truss samples based on these features. In this study, 26 initial features are defined, and a selection method is proposed to get a group of effective features that adequately represent the truss shapes. Each feature is defined as a dimensionless value to reflect one aspect of geometric shapes. It can be calculated using structural information such as node coordinates. The definition of the features can be as simple as height-span ratio (HSR), as shown in Equation (1). It can also be as complicated as symmetry rate (SyR), which describes the symmetry of structures, as defined in Equation (2). Figure 2 illustrates the calculation of symmetry rate. A truss structure is divided into two parts by the central axis. The overlapping area can be calculated by folding one part to the other along the central axis. Then, the ratio of the overlapping area to the maximum area of the two parts can be obtained. It is evident that the larger the ratio, the higher the similarity between the two parts, and the more symmetrical the truss structure. \[HSR=\frac{h_{\text{max}}}{L_{span}}, \tag{1}\]  
where \(h_{\text{max}}\) = maximum height of truss nodes, \(L_{span}\) = span of truss structures. \[SyR=\frac{S_{o}}{\text{max}(S_{L},S_{R})}, \tag{2}\]  
Figure 1: Sample population of truss structures. where \(S_{o}\) = overlapping area, \(S_{L}\) = area on the left side of the central axis, and \(S_{R}\) = area on the right side of the central axis. To find the effective features, the K-means clustering method [35] is applied to classify the sample population into nine groups. The classification is based on each truss feature separately. Note that the value of each feature is normalized to 0-1. In addition, the average and the standard deviation of the feature value for each group are calculated. A resulting graph (Figure 3) is plotted as an auxiliary evaluation tool, in which the truss samples belonging to the same group are collected. The truss features are evaluated one by one. Three structural designers were invited to participate in the evaluation process. There are three criteria to select an effective feature. Firstly, visually identifiable similarities should exist between the truss samples within the same group, whereas visually identifiable differences should exist between different groups. Secondly, the average for each group needs to be evenly distributed and the standard deviation needs to be as small as possible. Thirdly, suggestions from the designers need to be taken into account. Taking HSR as an example, Figure 3 shows a part of the resulting graph of the feature. The maximum height of truss samples gradually decreases from group 1 to group 9, whereas the samples in the same group have similar heights. On the other hand, the average for each group is evenly distributed between 0 and 1, and the standard deviation of each group is small. This indicates the good numerical performance of the feature. Furthermore, the designers had no objection to the definition of the feature and affirmed its value to structural design. Therefore, HSR is identified as an effective feature. After evaluating all the initial features, nine effective features are identified and included in a feature vector, summarized in Table 1.  
Figure 3: Part of the resulting graph of height-span ratio (HSR). Figure 2: Principle of symmetry rate. These features describe five geometric attributes of truss shapes (basic size, complexity, mid-span width, flatness, and symmetry), in which Number of Members (NM), Mid-span Clear Height (MCH), and Average Length of Web Members (AL) can be easily calculated from the basic structural information. Besides, other effective features are expressed by Equations (3)-(5).