The Application Of The Stability Of The Sequential Probability Ratio Test In The Mechanical Fault Diagnosis

With the rapid development of science and technology and the improvement of automation level, security and reliability of the mechanical system is becoming more and more prominent. It is increasingly significant that finding out the fault accuratly and timely, identificating the fault type, judging the fault damage degree and making the assessment and forecast. Mechanical fault diagnosis technology has become a valuable research project. The Sequential probability ratio test (SPRT for short) is a kind of hypothesis test method based on statistical theory. It has been widely used in the field of fault detection. It has been hailed as "one of the most powerful statistical thinking" and occupies an important position in the mathematical statistics. Zheng Zukang put forward the stability of hypothesis testing theory in1997that conducted in-depth analysis for the reliability of hypothesis test. In the paper, the Stability of Hypothesis Testing and the sequential probability ratio test are combined together skillfully, and the application of stability of the sequential probability ratio test in mechanical fault diagnosis is discussed.This paper mainly works on the following three aspects:First of all,assuming that before and after failure, system structure is certain and only parameters change,that is the fault being regarded as a mutation on the average,which bases on the definition of reget and error correction that were put forward by Zheng Zukang. Then make inspection analysis on fault, and discuss the stability of the test.Second,on the basis of theoretical analysis and derivation of limited sample size,determination of boundary point, form of OC function and the ASN function in the sequential probability ratio test, the stability of hypothesis testing and the sequential probability ratio test are combined together skillfully. The definition the stability of SPRT is deduced.The sequential probability ratio test is asymptotically0-reget and also asymptotic0-error correction.Finally, the detail steps is given about the application of stability of the sequential probability ratio test application in mechanical fault diagnosis, and the corresponding algorithm is established. It also discusses the stability of the gear box fault information mean under the condition that the sample capacity is normal distribution so that strengthen the stability of SPRT conclusion.