Benben Jiang

A combined canonical variate analysis and Fisher discriminant analysis (CVA-FDA) approach for fault diagnosis

Abstract This paper proposes a combined canonical variate analysis (CVA) and Fisher discriminant analysis (FDA) scheme (denoted as CVA–FDA) for fault diagnosis, which employs CVA for pretreating the data and subsequently utilizes FDA for fault classification. In addition to the improved handling of serial correlations in the data, the utilization of CVA in the first step provides similar or reduced dimensionality of the pretreated datasets compared with the original datasets, as well as decreased degree of overlap. The effectiveness of the proposed approach is demonstrated on the Tennessee Eastman process. The simulation results demonstrate that (i) CVA–FDA provides better and more consistent fault diagnosis than FDA, especially for data rich in dynamic behavior; and (ii) CVA–FDA outperforms dynamic FDA in both discriminatory power and computational time.

Simultaneous Identification of Bidirectional Path Models Based on Process Data

In multivariate systems, the causality relationships between any two different data variables and the corresponding path models are often unknown. In this paper, the identification of bidirectional path models of a bivariate system is investigated by extending the augmented UD identification (AUDI) algorithm proposed by Niu (1992) which can simultaneously identify the order and parameters for open-loop systems with unclear physical meanings of the even columns in the data matrix. To extract more information than the AUDI algorithm for identification of bidirectional path models, we develop a novel approach based on construction of the interleave data vector and UD factorization of the data matrix. The odd and even columns of the resulting data matrix correspond to the parameters of the forward and backward path models, respectively. Moreover, the information contained in the data matrix can be evaluated to determine the causality between the two data variables. The ARMAX process with white noise is first considered. The results are then extended to the case with colored noise. Simulation results are presented to show the effectiveness of our proposed methods.

Simultaneous identification of bi-directional paths in closed-loop systems with coloured noise

In this paper, a novel instrumental variable (IV) based identification method is proposed for closed-loop systems in the presence of coloured noise. The key technique lies in constructing an interleaved information matrix with respect to a multiple model structure formulated for the bi-directional paths. Then by utilizing UD factorization, all the parameter estimates for both forward and backward path models with orders possibly from zero to n , as well as the corresponding minimum loss function values, can be obtained simultaneously. Simulation results are provided to show the effectiveness of the proposed method.

Extended-AUDI method for simultaneous determination of causality and models from process data

To the best of our knowledge, there are few methods which can determine both causality and models from process data, although both of them are crucial in practical applications. The extended augmented UD identification (EAUDI) is an identification approach which does not need a priori causal relationship between variables in advance. In this method, however, the information contained in the augmented information matrix (AIM) is still not fully utilized and yet helpful for causality analysis, namely, whether the values of cross-regressive coefficients are sufficiently weak to be considered as insignificant. Based on this, the EAUDI method is further extended to detect causality from process data, and it can also provide models of all connecting paths simultaneously. Moreover, hypothesis testing (F-distribution) is proposed to verify the results of this approach (by testing cross-regressive coefficients). The effectiveness of the proposed method is demonstrated by numerical examples.

An Extended AUDI Algorithm for Simultaneous Identification of Forward and Backward Paths in Closed-Loop Systems

Abstract In closed-loop system identification, most of the existing methods only focus on the forward path, yet few on simultaneous identification of the forward and backward paths. Meanwhile, an augmented UD identification (AUDI) algorithm has been proved effective in open-loop system identification, but it only extracts the forward path information, while not including the backward path information provided in an augmented information matrix, which is helpful for the closed-loop system identification. In this paper, an extended AUDI (EAUDI) is proposed to simultaneously identify the model orders and parameters of both forward and backward paths of a closed-loop system. The conditions of identifiability and uniform convergence for closed-loop systems using the EAUDI algorithm are also given. The effectiveness of this algorithm is demonstrated by a numerical example.

Simultaneous structure and parameter identification of multivariate systems by matrix decomposition

Structure determination and parameter identification of multivariate systems are crucial but rather difficult issues in system identification. Due to the explosive growth of process data along with the scale increase of industrial processes, directional links between variables of such complex processes are often undistinguishable, which is indispensable to model structure determination but is often assumed to be known beforehand in most identification methods. In this article, a new modelling approach is developed to simultaneously estimate the model parameters and structures (including model orders as well as the directional links between different process variables) of multivariate systems. A vector auto-regressive (VAR) form is utilized as the model formulation in this algorithm. The key technique lies in constructing an interleaved information matrix with respect to a multiple model structure formulated for the VAR representation. Then by utilizing the upper diagonal factorization, all the parameter estimates of all path models with orders from zero to m, as well as the corresponding cost function values, can be obtained simultaneously. The effectiveness of the proposed method is demonstrated via a numerical example and a distillation column system.

Latent variable modeling approach for fault detection and identification of process correlations

Techniques for monitoring process correlation structures remain to be explored, whereas significant progress has already been achieved on the monitoring of process variables. In particular, typical methods for monitoring correlation structure changes are strictly based on the process information described by the covariance matrix, and lack the ability to effectively monitor underlying structure changes. In this paper, a new approach for fault detection and identification (FDI) of process structural changes is developed, which utilizes the regression technique of latent variable modeling (LVM) to abstract principal parameters as lower-dimensional representations of the parameters in the entire dimensionality. Apart from the enhanced performance of handling the underlying connective structure information, the proposed approach can also improve fault monitoring performance owing to the more accurate confidence intervals of the regression coefficients provided in the LVM step. The effectiveness of the proposed method for the detection and identification of correlation structure changes is demonstrated for both single faults and multiple faults in the simulation studies. In addition, the relationship between the FDI of process variables and correlation structures is discussed.

Locality preserving discriminative canonical variate analysis for fault diagnosis

Abstract This paper proposes a locality preserving discriminative canonical variate analysis (LP-DCVA) scheme for fault diagnosis. The LP-DCVA method provides a set of optimal projection vectors that simultaneously maximizes the within-class mutual canonical correlations, minimizes the between-class mutual canonical correlations, and preserves the local structures present in the data. This method inherits the strength of canonical variate analysis (CVA) in handling high-dimensional data with serial correlations and the advantages of Fisher discriminant analysis (FDA) in pattern classification. Moreover, the incorporation of locality preserving projection (LPP) in this method makes it suitable for dealing with nonlinearities in the form of local manifolds in the data. The solution to the proposed approach is formulated as a generalized eigenvalue problem. The effectiveness of the proposed approach for fault classification is verified by the Tennessee Eastman process. Simulation results show that the LP-DCVA method outperforms the FDA, dynamic FDA (DFDA), CVA-FDA, and localized DFDA (L-DFDA) approaches in fault diagnosis.

Dynamic Minimax Probability Machine-Based Approach for Fault Diagnosis Using Pairwise Discriminate Analysis

Fault diagnosis plays a key role in the safe and efficient operation of industrial processes. With the emerging big data era, the analytic methods based on probabilistic representations have attracted growing research interest. In this brief, a dynamic minimax probability machine (DMPM) approach based on the framework of probabilistic representations is proposed for diagnosing process faults, without imposing any assumptions on data distributions. In addition, an information criterion is put forward to determine the optimal dimensionality reduction order and time lags of DMPM. The proposed DMPM-based method allows for the enhanced performance of fault diagnosis due to the following advantages over conventional diagnostic approaches. First, DMPM maximizes the pairwise separation probability between each pair of faulty data sets, directly yielding improved discriminatory power in the projected space. Second, the proposed approach is less likely to be influenced by “outlier” classes since its objective function is a summation of probabilities, thereby enabling it to be beneficial for the classification of imbalanced data. Third, DMPM has superior capability on capturing dynamic information from the process data by augmenting observation vectors with time lags. The effectiveness of the proposed approach is demonstrated on the Tennessee Eastman process.

Pairwise discriminate analysis based minimax probability machine (PDA-MPM) approach for fault diagnosis

FauM diagnosis is crucial to maintain safe and efficient operations of industrial processes. In this paper, a minimax probability machine (MPM) approach based on the framework of probabilistic representations is put forward for diagnosing process faults, without imposing any assumptions on data distributions. Moreover, a technique of pairwise discriminate analysis is incorporated to handle the classification of multiple faulty datasets. In addition to the enhanced handling of imbalanced distribution of datasets, the proposed MPM-based approach can also bring the benefits for fault diagnosis, owning to the utilization of an objective function in the form of summation of the pairwise separation probabilities between each pair of faulty datasets. The effectiveness of the proposed approach is demonstrated on the benchmark of Tennessee Eastman process.