Relationships between PCA and PLS-regression

This work aims at comparing several features of Principal Component Analysis (PCA) and Partial Least Squares Regression (PLSR), as techniques typically utilized for modeling, output prediction, and monitoring of multivariate processes. First, geometric properties of the decomposition induced by PLSR are described in relation to the PCA of the separated input and output data (X-PCA and Y-PCA, respectively). Then, analogies between the models derived with PLSR and YX-PCA (i.e., PCA of the joint input-output variables) are presented; and regarding to process monitoring applications, the specific PLSR and YX-PCA fault detection indices are compared. Numerical examples are used to illustrate the relationships between latent models, output predictive models, and fault detection indices. The three alternative approaches (PLSR, YX-PCA and Y-PCA plus X-PCA) are compared with regard to their use for statistical modeling. In particular, a case study is simulated and the results are used for enhancing the comprehension of the PLSR properties and for evaluating the discriminatory capacity of the fault detection indices based on the PLSR and YX-PCA modeling alternatives. Some recommendations are given in order to choose the more appropriate approach for a specific application: 1) PLSR and YX-PCA have similar capacity for fault detection, but PLSR is recommended for process monitoring because present a better diagnosing capability; 2) PLSR is more reliable for output prediction purposes (e.g., for soft sensor development); and 3) YX-PCA is recommended for the analysis of latent patterns imbedded in datasets.Fil: Godoy, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Universidad Tecnológica Nacional. Facultad Regional Paraná; ArgentinaFil: Vega, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentina. Universidad Tecnologica Nacional; ArgentinaFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentin

Detecting stationary gain changes in large process systems

Stationary process gains are critical model parameters to determine targets in commercial MPC technologies. Consequently, important savings can be reached by acceding to an early prevention method capable of detecting whether the actual process moves away from the modeled dynamics or not, particularly by indicating when the process gains are not more represented by those included in the model identified during commissioning stages. In this first approach, a subspace identification method is used under open loop process condition to develop a process gain-matrix estimator. The main reason for using the subspace identification method is that it works directly with raw data and that the development is intended for monitoring future applications under multivariable closed-loop optimizing control where the transient regime is a frequent scenario. The objective of this paper is to present a method capable of detecting those gains of a multivariable model that start moving away from the original values. The anticipated knowledge of these events could provide a warning to process engineers and prevent from targeting process conditions with wrong gain estimations. The regular follow-up of the gain matrix should also help to localize those dynamics needing an updating identification.Fil: Bustos, Germán Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentin

New contributions to non linear process monitoring through kernel partial least squares

The kernel partial least squares (KPLS) method was originally focused on soft-sensor calibration for predicting online quality attributes. In this work, an analysis of the KPLS-based modeling technique and its application to nonlinear process monitoring are presented. To this effect, the measurement decomposition, the development of new specific statistics acting on non-overlapped domains, and the contribution analysis are addressed for purposes of fault detection, diagnosis, and prediction risk assessment. Some practical insights for synthesizing the models are also given, which are related to an appropriate order selection and the adoption of the kernel function parameter. A proper combination of scaled statistics allows the definition of an efficient detection index for monitoring a nonlinear process. The effectiveness of the proposed methods is confirmed by using simulation examples. Keywords: KPLS Modeling, Fault Detection, Fault Diagnosis, Prediction Risk Assessment, Nonlinear Processes.Fil: Vega, Jorge Ruben/ Universidad Tecnològica Nacional. ArgentinaPeer Reviewe

Referential process–reaction curve for batch operations

This paper shows an extension of the well-known process reaction curve method to empirically determine reduced-complexity models aimed to the design and tuning of feedback controllers for non-stationary batch processes. The basic idea is to isolate the dynamics associated to the manipulated variable from the main time-variable behavior that characterizes the operation, by taking the time evolution of a previous run as reference. One or more input-perturbed evolutions can then be compared to the previous dynamic pattern yielding referential reaction curves. This modeling approach cancels out most of the non-stationary behavior, allows capturing the dominant manipulated-variable dynamics and the use of available tuning rules for integrating systems. The effectiveness of this procedure is illustrated by using a nonlinear model of a bioreactor that simulates the production of Xanthan gum.Fil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

An extended MPC convergence condition

Nominal convergence of Constrained Model Predictive Control has been extensively analyzed in the last fifteen years. The inclusion of a terminal constraint into the optimization problem and the expansion of the prediction horizon up to infinity are the main strategies already proposed in order to achieve the desired stability. However, when a model is used in which the inputs are in the incremental form, these strategies tend to be infeasible. This paper extends the contracting constraint idea by including a simple-to-apply and less restrictive new set of constraints into the optimization problem, to allow nominal convergence.Fil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

Designing and tuning robust feedforward controllers

A model-based design and tuning procedure for feedforward controllers, which accounts for model uncertainties of SISO systems. Proper relationships for the analysis of feedforward-feedback control systems shows that tuning the feedforward controller is not completely independent form the feedback loop spectral characteristic. Similarly, fine tune of the associated feedback controller requires to be based on the residual disturbance remaining after the feedforward control action. Consequently, the simultaneous tuning is proposed for efficiently solving disturbance-rejection problems. Two application example show that the robust combined tuning gives satisfactory results for different dynamic and different tuning requirements.Fil: Adam, Eduardo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

Conceptual Modeling and Referential Control Applied To Batch Distillations

This paper proposes the combined use of a conceptual modeling method and a referential control strategy to operate batch distillation columns. Using the pinch theory, the modeling method, which is valid for multicomponent mixtures, allows the derivation of a quasi-optimal recipe to guide de operation properly. The referential control implies the empirical determination of reduced-order models for designing and tuning feedback controllers dedicated to tracking non-stationary conditions in batch processes. While defining a feasible recipe implies adjusting the reference trajectory until the desired product purity and recovery is achieved, defining the feedback control system implies first the selection of an appropriate tray temperature evolution, and then the isolation of the dynamics associated to the manipulated variable from the main time-variable behavior desired for the operation. The effectiveness of this combined procedure is illustrated through rigorous simulations where the light component is recovered from binary and ternary mixtures of alcohols.Fil: Espinosa, Hector Jose Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; ArgentinaFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

An integral approach to inferential quality control with self-validating soft-sensors

This paper presents an integral technique for designing an inferential quality control applicable to multivariate processes. The technique includes a self-validating soft-sensor and a multivariate quality control index that depends on the specifications. Based on a partial least squares (PLS) decomposition of the online process measurements, a fault detection and diagnosis technique is used to develop an improved self-validation strategy that is able to confirm, correct or reject the soft-sensor predictions. Model extrapolations, disturbances or sensor faults are first detected through a combined statistic (that considers the calibration region); then, a diagnosis is made by combining statistics pattern recognition, contribution analysis, and disturbance isolation based on historical fault patterns. An off-spec alarm is produced whenthe proposed index detects that an operating point lies outside the integral design space driven by thespecifications. The effectiveness of the proposed technique is evaluated by means of two numerical examples. First, a synthetic example is used to interpret the fundamentals of the method. Then, the techniqueis applied to the industrial Styrene-Butadiene rubber process, which is emulated through an available numerical simulator.Fil: Godoy, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico Para la Industria Química; Argentina. Universidad Tecnologica Nacional; ArgentinaFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico Para la Industria Química; ArgentinaFil: Vega, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico Para la Industria Química; Argentina. Universidad Tecnologica Nacional; Argentin

A fault detection and diagnosis technique for multivariate processes using a PLS-decomposition of the measurement space

A newstatisticalmonitoring technique based on partial least squares (PLS) is proposed for fault detection and diagnosis inmultivariate processes that exhibit collinear measurements. A typical PLS regression (PLSR) modeling strategy is first extended by adding the projections of the model outputs to the latent space. Then, a PLSdecomposition of the measurements into four terms that belongs to four different subspaces is derived. In order to online monitor the PLS-projections in each subspace, new specific statistics with non-overlapped domains are combined into a single index able to detect process anomalies. To reach a complete diagnosis, a further decomposition of each statistic was defined as a sum of variable contributions. By adequately processing all this information, the technique is able to: i) detect an anomaly through a single combined index, ii) diagnose the anomaly class from the observed pattern of the four component statistics with respect to their respective confidence intervals, and iii) identify the disturbed variables based on the analysis of the main variable contributions to each of the four subspaces. The effectiveness observed in the simulated examples suggests the potential application of this technique to real production systemsFil: Godoy, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Vega, Jorge Ruben. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); ArgentinaFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Desarrollo Tecnológico Para la Industria Química (i); Argentin

Predictive control applied to heat-exchanger networks

This paper discusses the online optimization and control of a heat-exchanger network (HEN) through a two-level control structure. The low level is a constrained model predictive control (MPC) and the high level is a supervisory online optimiser. Since MPC is a multivariable control technique capable of handling control-input constraints, it is neither necessary to define a variable-pairing approach nor to include individual loop-protections to avoid close-loop saturations. The proposed MPC algorithm uses an approximate linear model of the system to perform the output predictions and to account for the constraints. On the other hand, the supervisory program, based on a rigorous model, computes desired values to key manipulated variables of MPC, leading to minimum utility consumption. The coordination between the supervisory program and MPC is achieved through the definition of an extended cost-function that enables the controller to drive the system to the optimal operating condition. The proposed method was successfully tested by rigorous simulation of a typical HEN of the process industry.Fil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Odloak, Darci. Universidade de Sao Paulo; BrasilFil: Marchetti, Jacinto Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin