# Multi-Objective Pareto Optimization of Tensile Membrane Architecture for Energy Harvesting
## 4 Discussion
As shown in Figure 6, the performance of the same TMA type in different environments was investigated. The results of the Pareto solutions of each experiment are presented, grouped by  
Figure 5: Pareto-optimization results for Texas, USA. shape type and region. The performance of the TMAs in the same region and with the same shape type corresponding to the three wind patterns is visualized in Figure 6a-f graphs. Figure 6g-i graphs compares performance by region with the average acceleration value between Inner Mongolia and Texas. Inner Mongolia, which had a higher average wind speed, appeared to have a larger amount of electricity generated than Texas. In Texas, at a higher frequency, there was a higher probability for electricity to be generated. However, in Inner Mongolia, the electric generation was not proportional to the wind frequency. Moreover, the acceleration values of the low-frequency alternatives exceeded those of the high-frequency alternatives in Figure 6a. In the Inner Mongolia graphs, the acceleration values of the medium-frequency alternatives overtook the high-frequency alternatives at stiffness values of 1900 (hyper), 2300 (conic), and the whole (barrel vault), respectively. The results for China's medium-frequency alternatives indicate that the wind pattern plays an important role in the energy-harvesting performance of the TMA. As mentioned in Section 3.2, the wind direction (WindVector) and wind strength (Amplitude) values changed every 10 iterations. The value of WindVector varied every 10 iterations according to the region (Figure 1), regardless of the frequency, but the value of Amplitude varied every 10 iterations according to the frequency type (Figure 2). The experimental results suggest that when the WindVector changed significantly, the high-frequency wind speed was low (close to zero), and the medium-frequency wind speed was high; thus, the acceleration was high. Importantly, the results indicate that a high wind frequency does not necessarily correspond to a high energy efficiency. Table 2 shows the reduction rate from the largest acceleration value to the smallest acceleration value among the 30 th generation results in Figure 6. Since the reduction rate of hyper is much larger than those of the other two types, when designing hypers, it is recommended to determine the material stiffness as an extra consideration. The reduction rates of the conic and the barrel vault are about 20-30% thus, design focus on stability to prevent failure of the TMA seems more advantageous. The wind pattern affects the reduction rate without a specific rule. Design of a high energy efficiency TMA will need careful consideration of the wind pattern because it affects the acceleration value unexpectedly. Figure 6: Three different types of alternatives for the last generation. In Figure 7, based on this study's experimental results, virtual energy harvesting of TMAs was assumed, referring to existing TMAs. A total of three TMAs were determined for each shape type, and simulations were conducted to figure out their electric generation capacity. Information based on the TMAs in Figure 7 was used to define the shapes, thus, polyester fabric provided the material stiffness of Figure 7a,c and fiberglass provided the material stiffness of Figure 7b. The three wind-frequencies of Inner Mongolia and Texas were used, and the orientation was fixed to 0. The simulation result presented an average of acceleration values of three different wind-frequencies in the two regions as bar charts. The covered surface of Arabia Jeddah Airport is extraordinarily large, composed of 10 modules consisting of 21 tent units. If the airport were an energy harvestable TMA, its sustainability would be a big help to run the facility and the building owner would gain advantages. It might have also been possible to collect the ambient energy from the other two TMAs if they were designed as energy harvestable TMAs and if they made use of wasted energy.