# Multi-Objective Pareto Optimization of Tensile Membrane Architecture for Energy Harvesting
## 1 Introduction  
With the global concern about rising greenhouse-gas emissions due to fossil-fuel-based power generation, electricity production using eco-friendly energy sources is becoming increasingly important. Ambient or aeroelastic vibration--one of the eco-friendly energy sources being explored as an alternative to conventional fuel sources--has attracted the attention of many researchers over the past decade. The conversion of vibration into electricity is characterized mainly by electrostatic, electromagnetic, or piezoelectric transduction mechanisms, which can be used to obtain electricity through a variety of acquisition methods [1; 2; 3]. Studies on the conversion of vibration mechanical energy into electrical energy have been conducted using various types of vibration sources. These vibration sources can be from a variety of environments, including large architectural structures such as bridges, buildings, industrial equipment, home appliances, train railroads, cars, and airplanes [4]. Recently, following the trend of realizing autonomous energy-harvesting devices such as self-powered wireless sensors using roads, floor tiles, or bikes, the utilization of the vibration created by people has been investigated [5; 6; 7]. Among these sources, large architectural structures, such as bridges and buildings, utilize traffic-induced vibrations, seismic events, or wind-induced vibrations. They produce vibration-sourced electricity mainly through electromagnetic conduction mechanisms or mechanisms using piezoelectric materials. The tensile membrane architecture (TMA), which is the means of electricity production introduced in this paper, is an architectural structure that is classified into the same category of vibration sources as buildings and bridges but has not been utilized previously for vibration-generated electricity. It uses the same type of vibration that acts on a building or bridge and is characterized by energy collection using wind-induced vibration generated in the membrane. An example of electricity generation usinga membrane is the energy-harvesting eel developed by [PERSON] et al. [8], which confirms the feasibility of the energy-harvesting TMA. The TMA is a thin membrane structure with a unique surface shape and large deflection behavior that can support a structural load. TMAs are built in a wide range of sizes and for different purposes, including large structures, e.g., the Otto and Behnisch and Partners' Munich Olympic Stadium (1972), the traditional Mongolian ger, and a camping tent. An identifying feature of the TMA is that its entire structure (or part of it, such as a roof or wall) is wrapped with a tensile membrane cladding, such as fabric or foil. Compared to compression members, the most significant advantage of the TMA is that it can be as thin and as light as possible as long as the required prestress level is maintained [9]. Because of recent developments in technology and materials, a flatter shape rather than a highly curved shape for the architecture and adjusting the prestressing forces can be realized; and new attempts to develop TMAs are being made from existing research [10; 11]. The results from these studies indicate that as the technology advances, the application fields of TMAs will be expanded. Because TMA has a negligible bending and compression stiffness, the fluttering of the membrane is superior to that for typical building materials, resulting in an environment where ambient vibration or wind-induced vibration is likely to occur. The concept of generating electricity through the application of an energy-harvesting technique to the TMA was first presented in our previous paper [12]. In the present paper, we describe the optimization of energy-harvestable TMAs for two regions with the highest offshore wind-farm electricity production. The objective of this study was to determine which TMA geometry yields the optimal electricity generation and stability in a specific region.