(699c) ARX-Based Approach for Steady-State Identification Analysis of Industrial Processes

For the past decades, process systems engineering technologies, such as model predictive control (MPC) and real time optimization (RTO), have been employed to bring economic benefits to chemical processes. Along those lines, steady-state identification (SSI) approaches can help enhancing chemical processes by providing data for updating lumped parameters in stationary models, and by complementing other frameworks. For example, a classic steady-state RTO scheme crucially depends on SSI methodologies for its calculations, in order to update the parameters of the stationary model that represents various process operating conditions. The development and implementation of SSI methods have attracted much attention in numerous investigations¹, but present several challenges, including processing noisy irregular process data, errors Type I and II. In this work, a new SSI method based on the ARX (Auto-Regressive model with eXogenous inputs) technique is proposed and compared against other techniques from the literature via process systems examples.

            Steady-state analyses have been performed with different strategies in the literature. For example, Cao and Rhinehart² proposed a methodology, denoted as F-like test, based on the comparison of two variances for the determination of steady states. Bhat and Saraf³ extended the F-like test to consider the early determination of steady state and gross error detection in a crude distillation unit by means of tuning the critical values, implementing a linear Kalman filter, and performing data reconciliation by least-square techniques. Kelly and Hedengren⁴ developed a method for SSI to detect non-stationary drifts in chemical processes. Flehmig and Marquardt⁵ reported a technique which can infer trends in unmeasured states by using a linear process model. Jiang and coworkers⁶ derived a method that can find steady-state points employing wavelet theory. Yao and coworkers⁷ implemented a SSI methodology based on principal component analysis specific for batch processes. Finally, Le Roux et al.⁸ and Tao et al.⁹ proposed a technique based on a polynomial equation assuming a specified degree, and a moving window of data. Such techniques were employed for SSI by using the polynomial slope as index or critical value. Our proposed method in this presentation provides an alternative that permits the SSI with reduced tuning. This method considers a typical ARX model, in which the singularity of the model matrices is used as an index for steady-state determination.

            In this contribution, the F-like test², the polynomial-based approach⁹ and our proposed technique are implemented for SSI of two different cases. The first case considers a simulated data set in steady state and it is performed to evaluate the  techniques under simple conditions. The second case corresponds to a non-linear CSTR described in Pannocchia and Rawlings¹⁰ when operated at different steady states. During steady-state transitions, a non-linear model predictive control scheme is implemented to track set-point changes due to the non-linear characteristics of the system. For each case, we assume two white noise levels (with standard deviations equal to 3 and 5 % of the output value) that are typical of real industrial operating conditions. Results of these implementations show that the tuning of the F-like test and the polynomial-based methods is the most critical step for good performance of these approaches. Moreover, these techniques rely on an index that is sensitive to a user-defined threshold. On the other hand, our proposed approach depends on a mathematical index that characterizes the identifiability properties of the system and therefore can be implemented with reduced tuning. The conclusions of the analyses performed in these examples will facilitate the selection and implementation of the appropriate method for a depropanizer column owned by Petrobras S.A. with real industrial data.

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(4)      Kelly, J. D.; Hedengren, J. D. A Steady-state Detection (SSD) Algorithm to Detect Non-stationary Drifts in Processes. Journal of Process Control 2013, 23, 326.

(5)      Flehmig, F.; Marquardt, W. Inference of Multi-variable Trends in Unmeasured Process Quantities. Journal of Process Control 2008, 18, 491.

(6)      Jiang, T.; Chen, B.; He, X.; Stuart, P. Application of Steady-state Detection Method Based on Wavelet Transform. Computers & Chemical Engineering 2003, 27, 569.

(7)      Yao, Y.; Zhao, C.; Gao, F. Batch-to-Batch Steady State Identification Based on Variable Correlation and Mahalanobis Distance. Industrial & Engineering Chemistry Research 2009, 48, 11060.

(8)      Le Roux, G. A. C.; Santoro, B. F.; Sotelo, F. F.; Teissier, M.; Joulia, X. Improving Steady-state Identification. Proceedings of the 18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 2008, 25, 459.

(9)      Tao, L.; Li, C.; Kong, X.; Qian, F. Steady-state Identification with Gross Errors for Industrial Process Units. Proceedings of the 10th World Congress on Intelligent Control and Automation 2012, 4151.

(10)    Pannocchia, G.; Rawlings, J. B. Disturbance Models for Offset-free Model-predictive Control. AIChE Journal 2003, 49, 426.