Research On Fault Diagnosis And Performance Monitoring For Complex Industrial Systems Based On Riemannian Manifold Of Spd Matrices

With the development of globalization and commercial competition,the degree of automation of modern industry has been greatly driven by the rapid development of advanced technology,meanwhile the the process is becoming more and more complicated.Along with this trend is the uncertainties and perturbations which may lead to faults or abnormal operations of the process.As for complicated industrial process,due to the fact that its model is hardly known,data-driven monitoring and fault detection play a very important role of the safety,reliability and efficiency of the process under consideration.The conventional multi-variable analysis-based fault diagnosis poses many assumptions on the process,and it lacks the ability to detect multiplicative faults.Besides,it does not promise nice performance to nonlinear and dynamic systems.With regard to these observations,this paper is dedicated to data-driven performance monitoring and fault detection of processes with model uncertainties,multi modes,and dynamic systems behaviors.Firstly,analyzing the state of the art of multi-variable fault diagnosis technique,study their advantages and deficiencies on static systems,multi-mode systems,nonlinear systems,dynamic systems and sum up the key problems that remain open: 1)The mean and variance of the sampled data are not constant,the probability density function is hard to obtain,there are plenty sorts of faults in complex processes;2)The level of the noise and uncertainties are large,which pose un-uniformed impacts on the sampled data,incipient faults always be failed to be detected;3)It is difficult to distinguish uncertainties,multi modes,and faults in multi-mode process which is highly nonlinear.The key performance index is hard to obtain;4)Performance monitoring for dynamic systems with state feedback,as well as its control performance in complex processes.Secondly,a Riemannian metric based fault detection framework is proposed towards the unconstant mean and variance of the sampled data,unavailable pdf,and complex sorts of faults.This is the first application of Riemannian metric in the domain of fault diagnosis,in which Riemannian metric is adopted to build the performance index.It uses the Riemannian mean to cover the normal conditions and includes the uncertainties.Then the distance w.r.t.the Riemannian mean is computed to determine if faults occur.Additionally,the performance of the proposed index is analyzed in terms of uncertainty-to-fault detectability ratio.The results are compared with conventional methods which shows that the proposed method is efficient in detecting multiplicative faults and distinguish between uncertainties and faults.Thirdly,a developed Riemannian metric based method is proposed to solve the large level of noises,uncertainties,and un-uniform impacts on sampled data,also the problem of incipient fault detection in static system.And randomized algorithm aided threshold setting is proposed.Firstly,the weighted Riemannian metric is proposed,based on which the normalization is achieved by using its inverse as the weighting matrix.After the normalized Riemannian metric is obtained,the developed Riemannian metric-based method is obtained.On the other hand,randomized algorithm-aided threshold setting is also proposed for the threshold setting on symmetric positive definite matrix manifolds.Randomized algorithm-aided threshold setting is also proposed for normalized Riemannian metric.Fourthly,Riemannian metric based K means cluttering method is proposed w.r.t.multi modes,uncertainties,and faults which are hard to distinguish.It nicely distinguishes between uncertainties,faults,and multi modes in multi-mode processes,also be applied in to fault isolation/ classfication.Besides,a just-in-time learning Riemannian distance based method is proposed to solve the nonlinearity and unavailability of the process.By means of partial modelling,the nonlinearity is approximated,which solves the mixed problem of the complicated design parameters,heavy computation load.Fifthly,Riemannian metric based performance monitoring scheme for dynamic systems also be proposed.It is based on an SPD matrix solution of Lyapunov equation,and is proposed towards dynamic processes with state feedback.An SPD matrix can be identified from the input and output data,which indicates the dynamics of system and is later evaluated by the Riemannian metric for the purpose of performance monitoring.Extension application of other Riemannian metric based fault diagnosis results could also be employed and discussed.