# Multi-Objective Pareto Optimization of Tensile Membrane Architecture for Energy Harvesting
## 2 Related Works
### Membrane Energy Harvesting  
Because TMA is made of membrane materials such as fabric and foils, we introduce the possibility of energy harvesting via TMA by referring to a case where a membrane is used for energy harvesting. After this case is introduced, we discuss the studies referenced for our simulation, and propose a calculation method for the amount of energy harvested. The methods of energy harvesting via the membrane can be categorized into piezoelectric, triboelectric, and electromagnetic mechanisms. Through case studies involving these mechanisms, the conversion of various types of kinetic energy from motion into electrical energy, e.g., fluttering, bending, folding, rubbing, stretching, vibration, and pressure were examined. For example, the wind belt used by [PERSON] et al. [14] and the anchor-support-integrated membrane devices proposed by [PERSON] et al. [15] harvest energy from fluttering. The membrane triboelectric generators designed by [PERSON] et al. [16] and [PERSON] et al. [17] can harvest energy from human body movements, such as bending and rubbing. The piezoelectric cantilevers developed by [PERSON] et al. [18] and [PERSON] et al. [19] can be integrated into fabric to harvest energy from vibration. Different forms of kinetic energy, such as stretching, folding, and crumpling, can be converted into electric energy using the polyvinylidene dliuoride-based piezoelectric harvester proposed by [PERSON] et al. [20], piezoelectric strap proposed by [PERSON] and [PERSON] [21], and textile triboelectric generator proposed by [PERSON] et al. [22]. The fabric device proposed by [PERSON] et al. [23] can produce triboelectricity from water droplets. As indicated by the aforementioned works, electricity production using membranes is being actively studied. Selecting an optimal membrane-energy-harvesting device that converts a single form or mixed forms of kinetic energy in a specific TMA into electrical energy is also an important research subject, but the optimization of the generator type was not considered in this study. Instead of proposing how much electricity can be actually produced with a certain harvester, this study compares electricity generation of TMAs in different conditions and finds out the optimal TMA. Thus, simulations were designed with reference to studies related to wind-induced vibration-based energy harvesting. The type of harvester selected for the simulation was either a piezoelectric device integrated into a fabric or an electromagnetic device [14; 15]. Studies on wind speed estimation have been performed to evaluate the electricity generation via a TMA. In two studies, a wind speed probability distribution was created by analyzing site-monitoring results with different models to assess the wind energy [24; 25]. [PERSON] et al. [26] used an estimation algorithm that can estimate wind speed according to turbine measurement data to precisely predict wind speed in meters per second. However, to the best of our knowledge, there are no available wind speed data in meters per second for the areas covered in this paper. Similarly, it is impossible to obtain wind-fluttering patterns in seconds from Global Wind Atlas data, using an algorithm, and it was not in the scope of this study to infer local wind patterns through computational calculations using limited information. In summary, creating an actual wind environment is a complex and time-consuming task and needs sufficient wind data. In recent studies, researchers measured the wind speed using observation equipment and/or used algorithms to generate wind speed probability distribution estimation precisely [24; 25; 26]. Nonetheless, we lacked information to estimate the wind data. However, in the present study, because the fluttering of the membrane was essential for measuring the energy-harvesting performance of the TMA, we assumed a laboratory-scale periodic frequency blowing wind. A periodic wind pattern in the form of oscillation frequency was defined according to vibration-based energy-harvesting studies [7].