# Multi-Objective Pareto Optimization of Tensile Membrane Architecture for Energy Harvesting
## 3 Methodology
### Configuration for Genes: Wind Pattern  
This section explains in detail the process of defining the wind pattern of a target area. In the present study, the wind pattern corresponding to the \"Wind\" component of the simulation, which was a combination of the \"WindVector\" and \"Amplitude\" components, was derived from the 2019 data of the Global Wind Atlas [35]. To differentiate it from the previous paper [12] that did not consider the change of the WindVector, the Wind component was designed in consideration of the specificity of each region; the aim was finding a suitable TMA for the region. Figures 1 and 2 present the average annual wind speeds and wind directions measured at heights of 10 m in Inner Mongolia and Texas. The wind rose in Figure 1 indicates the horizontal direction probabilities in which the wind blew in a circular manner. The wind-direction value in the simulation was determined according to the probability of wind direction, and the WindVector parameter of the Wind component was then applied. Figure 2 presents the wind speed model applied to the experiment; a periodic wind pattern was used. This sine-shaped model started at the annual average wind speed value of the target region and had an amplitude equal to 50% of the annual average wind speed. However, Kangaroo performed the simulation according to a unit of time called \"iteration,\" which was different from the actual time; thus, the \(x\)-axis of the wind speed graph was based on iterations rather than the actual time. The program was set to perform 400 iterations per simulation, and accordingly, the period of the sine wave of the wind speed was classified into three types: low, medium, and high. Even in the same region, the wind frequency will be different depending on the surrounding environment, season, and time. Because this study did not focus on implementing the accurate wind pattern corresponding to each region, the wind pattern was simplified to present various environment conditions by using three different periodic frequencies. The focus was on the variation of the TMA performance for the same average wind speed and direction in the region. According to these types, the sine wave was drawn once, twice, and four times throughout the 400 iterations. Additionally, the speed, i.e., the y-axis of the wind speed graph, was converted into pressure (in Pascals) and applied as the Amplitude parameter of the Wind component. Therefore, Wind was the result of a combination of the wind direction, i.e., WindVector and the wind speed, i.e., Amplitude. All simulations were performed under the assumption that ambient conditions were negligible, to focus on the geometry under the given wind conditions. Figure 1: Wind-frequency roses for Inner Mongolia, China (**left**) and Texas, USA (**right**). The circular format of the wind rose shows the direction the winds blew from and the length of each “spoke” around the circle shows how often the wind blew from that direction. These wind roses do not provide the wind speed. For the implementation of the wind pattern, the Wind component consisting of the wind direction, i.e., WindVector, and wind speed, i.e., Amplitude, was set, and Kangaroo calculated the changes in the wind direction and speed over 10 iterations (Kangaroo's unit of time). Kangaroo counts 10 iterations by default when drawing a solution on the screen. Thus, assuming the actual time, like the wind direction and speed change once per second, the simulation was designed to change the wind direction and speed once per 10 iterations. The value of WindVector varied every 10 iterations according to the region (Figure 1), regardless of the frequency type, but the value of Amplitude varied every 10 iterations according to the frequency type (Figure 2). The default calculation value for drawing a solution was defined as 10 iterations; thus, 400 iterations were the time taken for Kangaroo to calculate a total of 40 TMA movements.