Research On Model And Data Driven System Identification And Fault Diagnosis Method In Gap Metric Model

In fault diagnosis research,taking different measures on residual information will have a crucial impact on models and data-driven methods.Although the Euclidean distance,usually used as a classic residual measurement method can reflect the degree of deviation of the system from normal behavior,it does not take the impact of the dimensions and the mean of each variable into consideration,resulting in poor fault diagnosis.To this end,we introduce a new measurement model called Gap,and carry out corresponding models and data-driven system identification and fault diagnosis research on the basis of the Gap.The main innovations in this paper are as follows.1)A fault detection and isolation method which is based on the principal component analysis in the Gap metric mode is proposed.Firstly,we extend the Gap metric based on from scalar space to vector space.Secondly,based on the constructed variable correlation coefficient matrix,a fault detection and isolation method which is founded on the principal component analysis in the Gap metric mode is established.Last but not least,the models of constant deviation and slowly changing micro-failure are respectively set up through the system,and simulations verify the effectiveness of the proposed method.2)The fault detection performance indicators and fault classification methods are established on the basis of the Gap metric.Firstly,with the help of the system's linear space representation and coprime factorization techniques,the concepts of kernel space and image space representation of the system are introduced,and the calculation of the Gap metric is transformed into a problem of the model matching in the system graph space.Secondly,the K-Gap induced by the system's nuclear space and the FDI framework composed of fault detectability,model uncertainty,and fault isolation indicators are studied so as to propose a fault classification method which is based on the model Gap metric.Finally,the model fault system which has been set up verifies the effectiveness of the FDI performance indicators and fault classification methods in this section.3)A data-driven dynamic system online fault diagnosis method based on the Gap measurement mode is established.First of all,the image space and kernel space representation methods of the system data-driven form are studied.Then,the Gap metric in a data-driven form which is obtained through the subspace identification method and the image space of the finite time series is used to approximate the model-based Gap metric.By constructing a multi-step prediction model,the calculation method of the real-time data-driven Gap metric is established.Last but not least,a simulation example verifies the equivalent consistency between the data-driven Gap metric and the model-based Gap metric and the effectiveness of the real-time calculation method.