本研究將探討壓力瓶在動態及與靜態的不確定因素影響下之可靠度最佳化設計。壓力瓶在RO逆滲透系統中是一重要元件，不但可儲存過濾後之純水也利用高壓隨時提供使用端充沛水量。然而製造及使用過程中的種種不確定因素，如加工的優劣及水壓的穩定性，導致最後設計可靠度不高，因此，本研究將壓力瓶兩本體間的焊接處強度視為隨機變數，並將施加於壓力瓶內側的水壓視為不確定因素的主要來源，期望壓力瓶在面臨破壞的狀況下仍舊可以保有90%以上的可靠度。
為了進行壓力瓶的可靠度最佳化設計，壓力瓶的幾何尺寸必須先加以參數化，並將其視為壓力瓶構形最佳化設計中的設計變數。設計優劣的評估，乃藉著建立反應曲面來近似於耗費資源的有限元素分析法。研究資料中顯示，高斯分佈足以適當的代表在壓力瓶上下半部之間焊接處強度的變化，而壓力負載的不確定因素則可用馬可夫鏈來模擬。以上所提到的模型均整合成一個同時具有與動態及與靜態的可靠度最佳化問題。為了詮釋動態系統限制式的可靠度，本研究使用第一次破壞時間(first passage time)及破壞率(crossover rate)的概念，並且比較其中的差異，而最終最佳化的結果，不僅僅能滿足可靠度要求同時與現今設計相比材料用量減少了高達46%。

Reliability-based design of a pressure tank under time-independent random and time-dependent stochastic uncertainties is considered. This pressure tank is an essential element in a reverse osmosis (RO) filtration system for storing filtered water and providing a useable flow rate from the faucet outlet. In this study,we consider the randomness in the welding strength be-tween the upper and lower tanks, and the stochastic pressure applied to the inner surfaces of the tank as the main sources of uncertainty. A pressure tank with 90% reliability against fracture failure is desired.To enable the re-design of the pressure tank, the geometry is parametrized and then used as design variables in a shape optimization scheme. Kriging models are created to approximate the expensive finite element analyses in accessing the performances of each design. The uncertainty model of the welding strength between the upper and lower tanks is found to be well represented by a Gaussian distribution. The stochastic behavior of the pressure loading is modeled by a Markov-chain process.All models are integrated in a reliability-based design optimization problem formulation that has both time-independent and time-dependent reliability constraints. The first passage time and crossover rate are considered in the time-dependent reliability constraint and results of different constraint formulations are compared. The final optimal design satisfies all reliability constraints and reduces the material usage by as many as 46% comparing to the original design.

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