Distributed partial least squares based residual generation for statistical process monitoring

Algorithms for partial least squares (PLS) modelling are placed into a sound theoretical context focusing on numerical precision and computational efficiency. NIPALS and other PLS algorithms that perform deflation steps of the predictors (X) may be slow or even computationally infeasible for sparse and/or large‐scale data sets. As alternatives, we develop new versions of the Bidiag1 and Bidiag2 algorithms. These include full reorthogonalization of both score and loading vectors, which we consider to be both necessary and sufficient for numerical precision. Using a collection of benchmark data sets, these 2 new algorithms are compared to the NIPALS PLS and 4 other PLS algorithms acknowledged in the chemometrics literature. The provably stable Householder algorithm for PLS regression is taken as the reference method for numerical precision. Our conclusion is that our new Bidiag1 and Bidiag2 algorithms are the methods of choice for problems where both efficiency and numerical precision are important. When efficiency is not urgent, the NIPALS PLS and the Householder PLS are also good choices. The benchmark study shows that SIMPLS gives poor numerical precision even for a small number of factors. Further, the nonorthogonal scores PLS, direct scores PLS, and the improved kernel PLS are demonstrated to be numerically less stable than the best algorithms. Prototype MATLAB codes are included for the 5 PLS algorithms concluded to be numerically stable on our benchmark data sets. Other aspects of PLS modelling, such as the evaluation of the regression coefficients, are also analyzed using techniques from numerical linear algebra.

A batch process is finite in duration and can be separated into two stages: startup and production. We develop a methodology to monitor a batch process during the startup stage to reduce the length of the startup stage. We focus on processes that are characterized by multiple process parameters and product characteristics. Because of the complex interdependencies characterizing the process parameters and product characteristics, it is more effective to evaluate them simultaneously. To address the multivariate nature of the process we use a multivariate statistical model: PLS (Projection to Latent Structures). PLS has been applied to several applications in statistical process monitoring. We present a new application of PLS to the startup stage of a batch process. Iterative adjustments made during startup in search of an acceptable production zone consume considerable amounts of material, labor and equipment time. We develop a monitoring procedure to reduce the time as well as the number of iterations and adjustments needed for startup. A PLS model is constructed, using baseline data, to characterize the relationship among process parameters during good production. The startup stage is monitored using the PLS characterization to determine if the process is consistent with good production. We illustrate the improved startup operations with an example from a batch process in filament extrusion, the application that motivates this work. Copyright © 2001 John Wiley & Sons, Ltd.

This paper proposes a common and individual (CnI) feature extraction-based process monitoring (PM) method for tracking the operating performance and product quality of processes with multiple operating modes. Different from traditional methods that separately develop PM models concerning only the individual feature of each mode data, the new method seeks to build the PM model simultaneously from all mode data, including to acquire the common subspace that captures the common feature behind different modes, and the individual subspace that reflects the unique feature of each mode. The newly proposed framework is achieved using the conventional principal component analysis (PCA) and partial least squares (PLS) based methods. The resulting CnI-PCA-based operating performance monitoring method and CnI-PLS-based product quality monitoring method are applied to the typical multimode finishing mill process (FMP) where common configuration for all steel products and individual setting for each steel are existing. Finally, the practical application result shows that the proposed method can be preferable to detect and identify different faults in the multimode FMP.

A weighted view on the partial least-squares algorithm

A Step-wise sequential phase partition algorithm with limited batches for statistical modeling and online monitoring of multiphase batch processes

Partial Least Squares (PLS) is a fault diagnosis model used in statistical process monitoring. PLS decomposes the data space into a quality correlated subspace and an uncorrelated subspace, and monitors the state of both subspaces by setting the appropriate statistics. However, post-processing methods such as modified-PLS (MPLS) and efficient projection to latent structures (EPLS) gradually lose their ability to detect faults when low-intensity faults that do not affect quality. In order to eliminate the drawbacks of post-processing methods and improve the stability of algorithms under different conditions, this paper introduces the competitive and adaptive reweighted sampling method (CARS) into the field of fault diagnosis and proposes a fault filtering method combining CARS and orthogonal signal correction algorithm (OSC). First, an initial screening of the variable space was completed using CARS method. OSC algorithm is then used to remove quality- uncorrelated components. Next, the variable space is completely decomposed into a quality-correlated and an irrelevant subspace using intensified partial least squares method (IPLS). Finally, the validity of the model was verified using the simulations.

Statistical process monitoring (SPM) methods have been adopted and studied to detect variations in the fused deposition modeling (FDM) process in recent years. The FDM process that builds parts layer-by-layer is accomplished in a specified manufacturing period (number of layers) without interruption or suspension. Thus, traditional SPM methods, where the average run length is used for the calculation of the control limits and the measurement of the performance, are no longer applicable to the FDM process. In this paper, an SPM method is proposed based on the surface image data of FDM parts with consistent layers and a specified period. The probability of alarm in a specified period (PASP) and the cumulative PASP are introduced to determine the control limits and evaluate the monitoring performance. Regions of interest are determined in a fixed way to cover the sizes and locations of different defects. The statistics are calculated based on the generalized likelihood ratio. The control limit is determined based on the specified period and the nominal in-control PASP. A simulation study for different locations, sizes and magnitudes of the mean shift of defects is presented. In the case study, the proposed SPM method is applied to monitor the FDM process of a cuboid, which verifies the effectiveness of the proposed method.

As a rapid and accurate technique, near infrared (NIR) spectroscopy has been widely used in process monitoring to improve efficiency and ensure quality consistency. In the present work, the application of NIR spectroscopy for on-line quantitative monitoring of the concentration process of Wangbi tablets was investigated. Partial least squares regression (PLSR) models based on the full-range spectra or the key wavelengths selected by the competitive adaptive reweighted sampling (CARS) method were established. The accuracy of the CARS-PLSR method was greater than that of full-spectrum PLSR for three quality parameters (soluble solid contents, paeoniflorin and icariin). For the prediction set samples using the CARS-PLSR models the coefficients of determination ( r2) and root mean square error [ RMSEP (%)] were 0.97 and 1.29 for soluble solid contents, 0.93 and 0.014 for paeoniflorin and 0.85 and 0.009 for icariin, respectively. Overall the results indicated that NIR spectroscopy coupled with CARS-PLSR calibration is a reliable and non-destructive alternative method for on-line monitoring of the concentration process of Wangbi tablets on an industrial scale.

Control charts and other related techniques for statistical process monitoring are in widespread use. The last 20 years have seen increasing emphasis on statistical process control as a practical approach to reducing variability in industrial applications. Simultaneously, there has been renewed interest in the subject by the academic and research communities. This has resulted in many new techniques and procedures, as well as better understanding of the performance and the limitations of well-established ones. This panel discussion is a technical discussion of control charts and other related methods for process monitoring. The panel consists of a group of researchers and practitioners who are involved in the development, evaluation, and application of these techniques. Topics considered by the panel include multivariate quality control, autocorrelated data, enhancements to the basic Shewhart control charts, economic design and related issues, and the relationship of statistical process monitoring and direct process adjustment through engineering control. The panel considers practical aspects of the application of these techniques as well as future trends in research and development.

Partial least squares (PLS) is a class of methods for modeling relations between sets of observed variables by using the latent components where the predictors are highly collinear. SIMPLS is a commonly used PLS algorithm that calculates the latent components directly as linear combinations of the original variables. However, SIMPLS is known to be very sensible to outliers since it is based on the empirical cross-covariance matrix. RoPLS is a recently proposed iterative method for robust SIMPLS. In this article, the influence function for the RoPLS coefficient estimator is derived. It is demonstrated that under certain conditions, the RoPLS estimator has infinitesimal robustness.

Data fusion methods for statistical process monitoring and quality characterization in metal additive manufacturing

Sparse partial least-squares regression and its applications to high-throughput data analysis

Combining convolutional neural networks and on-line Raman spectroscopy for monitoring the Cornu Caprae Hircus hydrolysis process.

Role of Excipients on Solid-State Properties of Piroxicam During Processing

Ultrasonic concentration measurement of aqueous solutions using PLS regression