中文摘要：

针对基于解析模型的非线性系统故障可诊断问题，提出了一种基于微分几何理论的故障可诊断判断方法。基于相对阶概念，定义了非线性系统的故障特征指数。对于单个故障单个输出的非线性系统，只要满足其故障特征指数小于等于系统的相对阶，就可证明故障是可以通过输出函数进行诊断的，即故障可诊断，并进一步证明了多输出非线性系统多个故障可诊断性的充要条件，同时进行可诊断性验证和数值模拟验证所提方法的有效性。

英文摘要：

A differential geometry approach was introduced to the problem of fault detection for a class of nonlinear systems based on analytical model‐based .Firstly ,characteristic index with the fault was defined based on relative degree .For single fault single output nonlinear systems ,the fault could be detected as long as relative degree of the system less than or equal to characteristic index with the fault .Then ,sufficient and necessary conditions were given for the fault detection and diagnosis for multi fault multi output systems .The approach was given and illustrated with a nonlinear system . Numerical simulations were carried out to verify the effectiveness of the proposed approach .