中文摘要：

从几何角度分析协同优化方法，并据此提出一种新的系统级优化模型，相对于代数分析，几何分析更简洁直观。分析学科级优化的几何意义，指出在学科级优化中最优设计点是距系统级提供的目标点最近的点，同时根据几何分析还能在该最优点处方便地获得主动约束边界的梯度，基于该最优点及此点处的梯度信息，可以构造出主动约束边界的一个线性近似并提供给系统级。随着迭代的进行，更多的线性约束将加入到系统级优化中，这一系列线性近似的组合构成的设计空间逐步逼近了原问题的设计空间。采用基于几何分析的协同优化方法对一齿轮减速箱进行优化设计，并将设计结果与传统协同优化方法的设计结果进行对比，研究结果表明，本方法在保持计算精度的前提下提高了计算效率。

英文摘要：

Geometric analysis of collaborative optimization （CO） algorithm is presented, based on which a new system-level optimization model is constructed. Compared with the algebraic analysis, the geometric analysis is more intuitive and concise, which shows that in the discipline-level optimization the optimal design point is the closest point to the target point provided by the system-level optimization. Moreover, the gradient of the active constraint boundary at the optimal design point can also be obtained through the geometric analysis. As a result, a linear approximation of the discipline-level active constraint can be constructed, which will then be passed to the system-level optimization to serve as system-level constraint. As the iteration goes on, more linear constraints will be added to the system-level optimization and the combination of these linear constraints can gradually approximate the feasible region of the original optimization problem. A gear reducer design problem is solved by using both the presented CO method and the conventional CO method, which shows that the presented method is more computationally efficient than the conventional one.