(183c) Advanced Data Analytics for Process-Shop Base+Delta Sub-Model Estimation in Planning and Scheduling Decision-Making

Typically, process data used for planning and scheduling is outdated or not properly integrated with the current state of the production, generating inconsistencies in the prediction of product streams in a chain-wide transformation throughout the manufacturing network [1]. Therefore, estimating accurate process transformation formulas to propagate feed and process characteristics into yields and properties of product streams is one of the major challenges facing any integrated plant when making planning and scheduling decisions. Due to uncertainties in proper transformation formula, feed quality, measured data, etc., high-fidelity modeling becomes unrealistic. For better process-shop predictions on their yields and properties, we propose new data analytics techniques combining reconciliation and regression into an estimation strategy.

This better process transformation modeling can be integrated in a continuous cycle to provide process feedback, aiming to remove the gap between the model prediction and the actual values in the plant. Thus, the use of data and information measured within automated systems leads to greater precision and higher model reliability, especially when using techniques of parameter estimation and data reconciliation for a better quality or integrity of the plant information [2]. A case study involving a reactor and a tank in a production chain was considered by Kelly and Zyngier [3], in which the gap between the modeled and the actual inventory or level of the tank can be reduced to zero by using parameter feedback from the process. According to the authors, the proposed example points out that differences between the planned and the actual values of the process do not necessarily result from task execution problems or measurement errors, since the absence of feedback makes it impossible to discern the difference between an inadequate model and problems in implementation of the operations. Franzoi et al. [4] recently introduced a complete crude-oil refinery blend scheduling problem and applied both data reconciliation techniques and parameter feedback to effectively optimize the complex process system. The authors solved the feedback strategy within an iterative mixed-integer linear and nonlinear programming (MILP-NLP) decomposition and highlighted the importance of properly integrating data to the decision automation core to cope with uncertainties, to reduce inaccuracies and to close the gap between predictions and productions.

In the proposed data analytics, by doing constrained and weighted least squares to fit better base+delta sub-models using data reconciliation and regression techniques, the reconciliation forces the yields to add up to the unity (or 100%) and the regression fits base and delta coefficients simultaneously across all yields. In this proposition, the method has the following protocol: 1) independent variable bases are taken as the averages/means from the plant trials, test runs, survey days or sample experiments; 2) the estimation of dependent yield variables is ran one-at-a-time to get the minimum sum-of-squares of residuals also known as the standard-error; 3) the one-at-a-time yield objective function values are divided by the number of observations or samples minus one in order to properly compute the base and delta variances by compensating for the nominal number of degrees-of-freedom. This also equalize or balance the objective function so that all dependent variables or output responses are weighted equally when their base and delta coefficients are estimated simultaneously. In addition to the base and delta coefficient variances, which easily translate into 95% statistical confidence-intervals, gross-error detection statistics for each yield (and property) deviation from its measured and actual values is also performed. It should be noted that when estimating the property base+delta’s sub-models, as there is no overall consistency relationship with the yields summing to unity, we simply regress each property separately.

[1] MENEZES, B. C.; KELLY, J. D.; GROSSMANN, I. E.; VAZACOPOULOS, A. Generalized Capital Investment Planning of Oil-Refineries using MILP and Sequence-Dependent Setups. Computers & Chemical Engineering, v. 80, p. 140-154, 2015.

[2] KELLY, J. D.; ZYNGIER, D. Unit-operation nonlinear modeling for planning and scheduling applications. Optimization and Engineering, p. 1-22, 2016.

[3] KELLY, J. D.; ZYNGIER D. Continuously improve the performance of planning and scheduling models with parameter feedback. In: Proceedings of the foundations of computer-aided process operations (FOCAPO), 2008.

[4] FRANZOI, R.E.; MENEZES, B.C.; KELLY, J.D.; GUT, J.W. Effective scheduling of complex process-shops using on-line parameter feedback in crude-oil refineries, Process Systems Engineering, 2018.