Multivariate Statistical Analysis Based Fault Detection And Diagnosis

Since modern production processes and equipments gradually show the characteristics of large and complex,and greatly increase the probability of failures,which not only brings great hidden trouble to the production continuity and equipment safety,but also causes serious consequences,such as environmental pollution and human casualties.Therefore,fault detection and diagnosis technologies are particularly important to ensure the stable operation of production and equipment.In addition,with the development of distributed control system and computer technology,process data have also become more abundant and accessible than ever before.Under this background,data-driven methods have been developed and applied rapidly,among them,multivariate statistical analysis methods can obtain useful information in process data by using variable projection strategy,and construct corresponding statistical indicators to realize fault detection and diagnosis,which have been widely concerned by scholars at home and abroad.Although multivariate statistical analysis based fault detection and diagnosis has attracted much attention,and a large number of theoretical research results and engineering applications have been obtained.There are still some problems need to be solved.For example,how to do the plant-wide fault detection and diagnosis for large-scale dynamic process better,how to improve the interpretability of diagnosis model,how to use the samples information comprehensively,how to solve the small sample size problem,multimodality and nonlinearity problem and so on.Therefore,based on the existing research results,considering the complex characteristics of process data and aiming at the shortcomings of existing methods,some improved multivariate statistical analysis based fault detection and diagnosis methods are proposed.The main contents of this paper include:1.A distributed fault detection method based on variables partitioning and Bayesian inference is proposed in view of the limitation that centralized models are difficult to realize fault detection for large-scale dynamic processes.Considering that the process mechanism knowledge is not always available,the minimal redundancy maximal relevance algorithm is firstly used to accurately describe the correlations between the process variables and reduce the redundancy among them,which provides the optimal variable input for the base models.Then,the Bayesian inference is utilized to fuse the detection results in all sub-blocks into a comprehensive decision index so as to realize the distributed fault detection of the plant-wide processes.On this basis,a fault diagnosis criterion based on sub-block contribution is proposed,which translates fault diagnosis directly into locating the sub-block that contributes the most to current fault,and unaffected by overly enlarged data dimensionality.Finally,in order to avoid some variables being discarded by the artificial threshold,different weights are assigned to the variables in the augmented matrix according to the values of the minimal redundancy maximal relevance,so that the dynamic characteristics of the current variables can be described more comprehensively,which is helpful to improve the fault detection performance of the model.2.Considering the fact that Fisher discriminant analysis is difficult to handle the multimodality and nonlinear characteristics of the measured data,and the model interpretability is also poor,the sparse(kernel)local Fisher discriminant analysis is established.Since the process data often show multimodality properties,thus causing Fisher discriminant analysis infeasibility.Firstly,a local weighting factor is introduced into the scatter matrix to preserve the multimodality within measured samples.In addition,the elastic net algorithm is introduced into local Fisher discriminant analysis model,then the corresponding faulty variables can be identified automatically.And the optimal discriminant directions can be obtained by solving the current optimization problem through feasible gradient direction method.After that,the local data structure characteristics are exploited from both the sample-dimension and variable-dimension.So that the fault classification accuracy and the interpretability of the model are significantly improved.Besides,we extend the proposed sparse local Fisher discriminant analysis model to its nonlinear variant(i.e.,sparse kernel local Fisher discriminant analysis)by kernel trick,which can deal with the strong nonlinear characteristic of the process data.3.For single supervised or unsupervised multivariate statistical analysis methods are unable to make comprehensive use of labeled and unlabeled sample information,a fault detection and diagnosis method based on semi-supervised learning is proposed.It first introduces the labeled samples into the objective function of principal component analysis model,and a semisupervised principal component analysis model is proposed,which takes advantage of the useful information contained in labeled and unlabeled samples simultaneously,the proposed method is also more practical and robust.Then,the scatter matrixes in the supervised local Fisher discriminant analysis model are regularized to establish the semi-supervised local Fisher discriminant analysis model,so that the discriminant information in the labeled samples can be learned and the global structure of the whole data set can be retained,which provides comprehensive discriminant information for the fault classification model.In addition,the matrix exponential strategy is introduced to the semi-supervised local Fisher discriminant analysis model,which not only enlarges the margin distance between different classes and improves the classification performance of the model,but also guarantees the invertibility of scatter matrixes,thus the small sample size problem is solved well.And the application scenarios of the method are extended.The above methods provide new solution to fault detection and diagnosis problems in production and equipment operation.And the operation data of 6S35ME-B9 marine diesel engine and various simulation data(Tennessee Eastman process and numerical cases)are used for simulation verification,and compared with the existing methods,the experimental results demonstrate the effectiveness and practicability of the proposed methods.