利用极大值原理确定系统故障检测门限

On Determining Failure Detection Thresholds with the Maximum Principle

基于ＨｏｒａｋＤＴ的ＲＭＩ故障检测算法，提出了一种估算系统故障检测门限的方法，根据已知的系统模型和系统噪声水平，利用极大值原理离线估算被检测系统的故障门限。仿真计算表明本方法可有效用于新型飞机等难以获得大量实验数据的系统的故障检测问题。由于门限是离线确定的，基于此方法的故障检测算法实际运算量远小于ＲＭＩ算法。

For complex systems, such as new type aircraft, there exists the need of determiningfailure detection thresholds from indirect data, which are usually abundantly available. Webelieve we are the first to present the research results in published form about how to satisfythis need.We express the usually abundant indirect data in terms of boundaries of noises in themodel of the complex system. Then we construct a performance index, which is a useful ideawe take from Horak's paper[1] and give it as eq. (6). We employ the Maximum Principleto determine the variations of boundaries of the performance index with time. Under certainconditions, we prove that either of the boundaries of the performance index approaches aconstant as given in eq. (19). These two constants can be taken as upper and lower failuredetection thresholds. With these thresholds, we can estimate the boundaries of the outputsof the system with no failure.We take a certain aircraft as example. Simulation results give Fig. 2 which shows theoutput boundaries and the actual output. As the output boundaries are very close, it can besaid that failure detection thresholds are determined with good precision. When real responseoversteps the boundaries, the appearance of f&ilures is immediately detected. Thus, this numerical example indicates that our method is both accurate and practicable.