Ahmed Shokry

Applying Metamodels and Sequential Sampling for Constrained Optimization of Process Operations

This paper presents a framework for nonlinear constrained optimization of complex systems, in which the objective function and the constraints are represented by black box functions. The proposed approach replaces the complex nonlinear model based on first principles with Kriging metamodels. Coupled to Kriging, the “Constrained Expected Improvement” technique and a sequential sampling strategy are used to explore the metamodels, in order to find global solutions for the constrained nonlinear optimization problem. The methodology has been tested and compared with classical optimization procedures based on sequential quadratic programming. Both have been applied to three mathematical examples, and to a case study of chemical process operation optimization. The proposed framework shows accurate solutions and significant reduction in the computational time.

Application of Pricing Policies for Coordinated Management of Supply Chains

Abstract An optimization approach is proposed to coordinate multi-site multi-product SC networks taking into account the cooperation between suppliers and production/distribution SCs. For this purpose, all the interacting entities are integrated into the optimization model as full SCs, so any production/distribution echelon/SC can work as supplier for any other echelon/SC and so on. Financial issues based on price elasticity of demand, usually considered in these models just at the final SC echelon (end product), are incorporated in the proposed model at all interacting levels, so cost is subject to the trade-off between the price and the quantity demanded. Different approximations to model this demand elasticity have been tested, and the resulting NLP/MINLP models have been applied to a case study where the coordination of service (energy generation) SCs and production/distribution SCs is proposed. The results prove that pricing policies management add to PSE an additional instrument towards improving decision making.

Multiparametric metamodels for model predictive control of chemical processes

This work proposes a Data-Based MultiParametric-Model Predictive Control (DBMPMPC) methodology, which enables simple implementations of explicit MPC in situations when the deep mathematical knowledge required to develop traditional MP-MPC techniques is not available. Additionally, it can also assist in situations when it is difficult to apply traditional MP-MPC, due to the process model complexity or high nonlinearity. The proposed method uses machine learning techniques (Ordinary Kriging (OK), Support Vector Regression (SVR) and Artificial Neural Networks (ANN)), which are trained offline using input-output information. During the online application, the optimal control is calculated through simple interpolations using these multiparametric metamodels, avoiding the need for dynamic optimization. The method is tested with benchmark problems used in the MP-MPC literature. The results show high accuracy and robustness using a simple method, bypassing complex mathematical formulations.

Optimization Under Uncertainty Based on Multiparametric Kriging Metamodels

Different reasons can hinder the application of multiparametric programming formulations to solve optimization problems under uncertainty, as the high nonlinearity of the optimization model, and/or its complicated structure. This work presents a complementary method that can assist in such situations. The proposed tool uses kriging metamodels to provide global multiparametric metamodels that approximate the optimal solutions as functions of the problem uncertain parameters. The method has been tested with two benchmark problems of different characteristics, and applied to a case study. The results show the high accuracy of the methodology to predict the multiparametric behavior of the optimal solution, high robustness to deal with different problem types using small number of data, and significant reduction in the solution procedure complexity in comparison with classical multiparametric programming approaches.

Kriging based fault detection and diagnosis approach for nonlinear noisy dynamic processes

This paper presents a hybrid approach to enhance the performance of the data-based Pattern Classification Techniques (PCTs) used for Fault Detection and Diagnosis (FDD) of nonlinear dynamic noisy processes. The method combines kriging metamodels with PCT (e.g. Support Vector Machines). The metamodels are used in two different ways; first, they are used as Multivariate Dynamic Kriging(s) (MDKs) which estimate the process dynamic behavior/outputs, second, as classical static models which are used for smoothing noise and imputing missing values of the process actual outputs measurements. So during the process operations, the estimated and the smoothed actual outputs are compared, and residual/error signals are generated that is used by the classifier to detect and diagnose the process possible faults. The method is applied to a benchmark case study, showing a high enhancement in such PCTs due to the introduction of the process dynamics information to these PCTs via the MDKs, and by smoothing the noise and imputing the missing measurements using the static kriging.

Optimal Features Selection for Designing a Fault Diagnosis System

Abstract Fault diagnosis (FD) using data-driven methods is essential for monitoring complex process systems, but its performance is severely affected by the quality of the used information. Additionally, processing huge amounts of data recorded by modern monitoring systems may be complex and time consuming if no data mining and/or pre-processing methods are employed. Thus, features selection for FD is advisable in order to determine the optimal subset of features/variables for conducting statistical analyses or building a machine-learning model. In this work, features selection are formulated as an optimization problem. Several relevancy indices, such as Maximum Relevance (MR), Value Difference Metric (VDM), and Fit Criterion (FC), and redundancy indices such as Minimum Redundancy (mR), Redundancy VDM (RVDM), and Redundancy Fit Criterion (RFC) are combined to determine the optimal subset of features. Another approach of features selection is based on the optimal performance of the classifier, which is achieved by a classifier wrapped with genetic algorithm. Efficiency of this strategy is explored considering different classifiers, namely Support Vector Machine (SVM), Decision Tree (DT), K-Nearest Neighbours (KNN) Classifier and Gaussian Naive Bayes (GNB). A Genetic algorithm (GA), as a Derivative Free Optimization (DFO) technique, has been used due to the robustness to deal with different kinds of problems. The optimal subset of obtained features has been tested with SVM, DT, KNN, and GNB for the Tennessee-Eastman process benchmark with 19 classes. Results show that, when the performance of the classifier is used as the objective function the wrapper method obtains the best features set.

Modeling and Simulation of Complex Nonlinear Dynamic Processes Using Data Based Models: Application to Photo-Fenton Process

This paper investigates data based modelling of complex nonlinear processes, for which a first principle model useful for process monitoring and control is not available. These empirical models may be used as soft sensors in order to monitor a reaction’s progress, so reducing expensive offline sampling and analysis. Three different data modelling techniques are used, namely Ordinary Kriging, Artificial Neural Networks and Support Vector Regression. A simple case is first used to illustrate the problem, assess and validate the modelling approach, and compare the modelling techniques. Next, the methodology is applied to a photo–Fenton pilot plant to model and predict the reaction progress. The results show promising accuracy even when few training points are available, which results in huge savings of time and cost of the experimental work.

Mixed-Integer MultiParametric Approach based on Machine Learning Techniques

This paper investigates the extension of a MultiParametric approach based on surrogate models (Meta-MultiParametric approach, M-MP) in order to handle general Mixed- Integer (MI) optimization problems involving Uncertain Parameters (UPs). The method harnesses metamodeling and clustering techniques in order to approximate black box relations between the optimal values of the continuous variables and the UPs, while Classification Techniques (CT) are employed to identify the optimal values of the integer variables also as a function of the UPs. The results of applying the method to a benchmark case-study show a high prediction accuracy of the optimal solutions, saving computational effort and overpassing the complex mathematical procedures required by the standard MultiParametric Programming methods.

Imputation of Missing Data with Ordinary Kriging for Enhancing Fault Detection and Diagnosis

Abstract This work investigates the application of different metamodeling techniques for enhancing the information quality of the process history databases, through smoothing the noise/outliers and imputing missing data that usually contaminate such databases. The information quality enhancements are aimed at improving the training of the data-driven classification techniques used for Fault Detection and Diagnosis (FDD) of the process. A simulation case study of a Continuous Stirred Tank-Reactor (CSTR) is used to produce training datasets containing noisy, outlier and missing values. Three metamodeling techniques namely; Ordinary Kriging (OK), Artificial Neural Networks (ANN) and Polynomial Regression (PR) are used to smooth the noise and outliers, and to impute the missing values. Next, the FDD performance of the Support Vector Machines (SVM) classifier is compared when it trained with the recuperated datasets by the metamodels, while datasets have noisy, outlier and missing values. The results show high enhancement in the performance of the SVM when it trained with the recuperated data using the metamodels, especially when OK is exploited.

Data-driven soft-sensors for online monitoring of batch processes with different initial conditions

Abstract A soft-sensing methodology applicable to batch processes operated under changeable initial conditions is presented. These cases appear when the raw materials specifications differ from batch to batch, different production scenarios should be managed, etc. The proposal exploits the capabilities of the machine learning techniques to provide practical soft-sensing approach with minimum tuning effort in spite of the fact that the inherent dynamic behavior of batch systems are tracked through other online indirect measurements. Current data modeling techniques have been also tested within the proposed methodology to demonstrate its advantages. Two simulation case-studies and a pilot-plant case-study involving a complex batch process for wastewater treatment are used to illustrate the problem, to assess the modeling approach and to compare the modeling techniques. The results reflect a promising accuracy even when the training information is scarce, allowing significant reductions in the cost associated to batch processes monitoring and control.