本論文提出非線性以及線性化之二輪車輛數學模型，此模型可用以模擬二輪車運動行為及分析其穩定性。一無人駕駛之二輪車輛本身具有不穩定之特性，在高速行駛中，駕駛者難以控制其不穩定行為，因此我們利用最佳化及可靠度設計方法設計出一具有良好穩定性表現之二輪車。二輪車系統具有複雜的動態特性，本論文使用拉格朗方程式(Lagrange’s equation)推導二輪車輛之數學模型，為了詳細探討二輪車參數對於穩定性之影響，此二輪車由五個車身所建構，分別是後車輪、後車架、引擎、前車架以及前車輪，我們使用此數學模型探討不同車型之穩定性表現，包含了腳踏車、速克達及摩托車，並利用一次一因子方法(one-factor-at-a-time)得到參數敏感度結果，並找出二輪車輛之重要設計參數，其對應到各不穩定行為，分別為傾覆(capsize)、搖擺(weave)、及晃動(wobble)，我們使用這些重要設計參數與最佳化方法改善二輪車之穩定性，最佳化之二輪車輛在穩定性上有顯著的改善。本論文使用一次二階矩(first order second moment)及蒙地卡羅(Ｍonte Carlo simulation)方法討論重要參數之不確定性對於二輪車穩定性的影響，為了使二輪車輛有更良好之穩定性表現，我們使用以可靠度為基礎之最佳化設計方法(reliability-based design optimization)設計一具有可靠穩定性表現之二輪車輛。期望此設計方法能應用於二輪車輛之開發上，增加駕駛者騎乘之安全性。

This thesis presents a fully nonlinear and linearized two-wheeled vehicle model for stability investigation. A two-wheeled vehicle is naturally unstable. When a unstable motion occurs in high speed driving, it is beyond a rider's control. We present a two-wheeled vehicle with high speed stability based on optimization and reliability design methods. To cope with the complex dynamic properties of two-wheeled vehicles, we apply Lagrange’s equations to construct the mathematical model. To study the influence of vehicle geometry and mechanical properties on stability in detail, five bodies are used to compose the vehicle. With the two-wheeled vehicle model, stability and sensitivity analyses are conducted for three representative types of vehicle, namely, a bicycle, a scooter, and a motorcycle. The significant parameters corresponding to the most important unstable motions (weave and wobble) are identified. We focus on improving the stability performance in straight driving. The vehicle with optimized parameters has a significant improvement of stability. The influence of parameter uncertainty on stability is further studied by using the first order second moment (FOSM) and Monte Carlo simulation (MCS) methods. The MCS method is further employed in a reliability-based design optimization (RBDO) model for an accurate stability prediction. We expect that the RBDO method can be applied for two-wheeled vehicle design to avoid the unstable motions in high speed driving.

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