A novel quality-related statistical process monitoring method based on global and local partial least-squares projection (QGLPLS) is proposed in this paper. The main idea of the QGLPLS method is to integrate the advantages of locality-preserving projections (LPP) and partial least squares (PLS) and extract meaningful low-dimensional representations of high-dimensional process and quality data. QGLPLS can exploit the underlying geometrical structure that contains both global and local information pertaining to the sampled data, including the process variable and quality variable measurements. It is well-known that the PLS method can find only the global structure information and ignores the local features of data sets and that the LPP method can preserve local features of data sets well without considering the product quality variables. The capacity for the preservation of global and local projections of the proposed method is compared to that of the PLS and LPP methods; the comparison results demonstrate that the QGLPLS method can effectively capture meaningful information hidden in the process and quality data. Next, a unified optimization framework, i.e., global covariance maximum and local graph minimum in the process measurement and quality data space, is constructed, and QGLPLS-based T 2 and squared prediction error statistic control charts are developed for online process monitoring. Finally, two typical chemical processes, the Tennessee Eastman process and the penicillin fermentation process, are used to test the validity and effectiveness of the QGLPLS-based monitoring method. The experimental results show that the obtained process monitoring performances are better than those when using traditional monitoring methods, such as PLS, principal component analysis, LPP, and global–local structure analysis.

Nonlinear partial least-squares (NPLS) is widely used in quality-relevant process control and fault diagnosis for strongly nonlinear systems; however, the existing NPLS approaches suffer from various disadvantages. This study proposes a novel statistical model based on locality-preserving partial leastsquares (LPPLS) to enhance the processing capacity for system nonlinearity. The main concept of the LPPLS model is to utilize the locality-preserving projection to extract the principal components and preserve nonlinearities within the partial leastsquares (PLS) process. The intuitive presentations for three types of LPPLS models are established within the proposed framework for strongly nonlinear systems, in which the process variables can correlate nonlinearly with each other and with the quality variables simultaneously. A canonical algorithm, which is easily applied in actual processes and is similar to the traditional linear PLS, is deduced to extract the principal components. Then, a quality-related monitoring strategy is established based on the LPPLS model. The experimental results from an artificial test data set and the Tennessee Eastman process (TEP) benchmark demonstrate that the proposed method can maintain as much of the local properties of the original data as possible and yield good monitoring results for quality-relevant faults.

This paper investigates the stabilisation problem and consider transient optimisation for a class of the multi-inputmulti-output (MIMO) semi-linear stochastic systems. A control algorithm is presented via an m-block backstepping controller design where the closed-loop system has been stabilized in a probabilistic sense and the transient performance is optimisable by optimised by searching the design parameters under the given criterion. In particular, the transient randomness and the probabilistic decoupling will be investigated as case studies. Note that the presented control algorithm can be potentially extended as a framework based on the various performance criteria. To evaluate the effectiveness of this proposed control framework, a numerical example is given with simulation results. In summary, the key contributions of this paper are stated as follows: (1) one block backstepping-based output feedback control design is developed to stabilize the dynamic MIMO semi-linear stochastic systems using a linear estimator; (2) the randomness and probabilistic couplings of the system outputs have been minimized based on the optimisation of the design parameters of the controller; (3) a control framework with transient performance enhancement of multi-variable semi-linear stochastic systems has been discussed.

The partial least-squares (PLS) method is widely used in the quality monitoring of process control systems, but it has poor monitoring capability in some locally strong nonlinear systems. To enhance the monitoring ability of such nonlinear systems, a novel statistical model based on global plus local projection to latent structures (GPLPLS) is proposed. First, the characteristics and nature of global and local partial least-squares (QGLPLS) are carefully analyzed, where its principal components preserve the local structural information in their respective data sheets as much as possible but not the correlation. The GPLPLS model, however, pays more attention to the correlation of extracted principal components. GPLPLS has the ability to extract the maximum linear correlation information; at the same time, the local nonlinear structural correlation information between the process and quality variables is extracted as much as possible. Then, the corresponding quality-relevance monitoring strategy is established. Finally, the validity and effectiveness of the GPLPLS-based statistical model are illustrated through the Tennessee Eastman process simulation platform. The experimental results demonstrate that the proposed model can maintain the local properties of the original data as much as possible and yield monitoring results that are better than those of PLS and QGLPLS.

A novel statistical model based on a locally linear embedding projection to latent structure (LLEPLS) is proposed, which not only has a concise expression and similar analytical solutions to the projection to latent structure (PLS) model but also has the ability to maintain the local geometric structure of the locally linear embedding (LLE) model. Furthermore, to eliminate the adverse effects of oblique decomposition, a locally linear embedding orthogonal projection to latent structure (LLEOPLS) model is also proposed. The input and output data spaces are projected to three subspaces, namely, a joint input−output subspace that captures the nonlinear relationship between the input and output, an output-residual subspace that monitors the unpredictable output faults, and an orthogonal input-residual subspace that detects the quality-irrelevant faults. Then, the corresponding monitoring strategies are established based on the LLEPLS and LLEOPLS models. The Tennessee Eastman process (TEP) benchmark is used to illustrate the nonlinear mapping ability and effectiveness of the monitoring on quality-relevant and process-relevant faults of the proposed methods.