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摘要: 对于现代复杂控制系统, 微小故障往往很难发现. 在系统过程干扰和测量噪声未知但有界的前提下, 提出了一种新的基于状态集员估计的主动故障检测方法. 首先设计全对称多胞形卡尔曼滤波器对系统状态进行估计, 并利用全对称多胞形对受未知干扰影响的状态集合进行描述, 然后设计辅助输入信号使得加入辅助输入信号后正常模型的状态集合与故障模型的状态集合交集为空, 从而实现主动故障检测. 为了使得所设计的辅助输入信号对原系统影响最小, 需要求得最小的辅助输入信号, 本文将最优化问题转化为混合整数二次规划问题进行求解. 最后, 与基于输出集合的辅助输入信号设计方法对比, 仿真验证本文所提出的基于状态集合的主动故障检测方法由于未受下一时刻测量噪声的影响, 所求得的辅助输入信号更小, 保守性更低.Abstract: For modern complex systems, incipient faults is usually difficult to be detected. Under the assumption that system process disturbance and measurement noise are unknown but bounded, this paper proposes a novel active fault detection method based on state set-membership estimation. First, a zonotopic Kalman filter is designed to estimation systems states, and the state sets affected by the unknown inputs are described by zonotopes. Then, an auxiliary input signal is designed such that the state sets of the normal model are separated from the ones of faulty models, as a result, incipient faults are detected successfully. In order to decrease the effect of the auxiliary input to the practical systems, the minimum auxiliary input signal is required. In this paper, the optimization problem is transformed into a mixed integer quadratic programming problem. Compared with the output sets based auxiliary input signal design method, the proposed technique can achieve a smaller auxiliary input signal because of states set are not affect by the measurement noise at the next time instant, and it has less conservatism.
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Key words:
- Active fault detection /
- state set-membership estimation /
- auxiliary input signal /
- zonotope /
- incipient fault
1) 本文责任编委 辛景民 -
图 1 在正常模型和故障模型下, 加入辅助信号与未加辅助信号结果的对比
Fig. 1 Comparison of the results of adding auxiliary signals and unassisted signals under normal and fault models
图 2 在正常模型和故障模型下, 加入辅助信号对状态和输出的影响
Fig. 2 The effect of adding an auxiliary signal on state and output under normal and fault models
图 4 加入辅助信号和未加辅助信号对系统输出的影响
Fig. 4 Effect of adding auxiliary signal and unassisted signal on system output
图 5 状态多胞形: 通过状态交集为空的方法
Fig. 5 Zonotope of the system state: the method of emptying the state intersection
图 7 输出多胞形: 通过输出交集为空的方法
Fig. 7 Zonotope of the system output: the method of emptying the output intersection
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