Fluid
catalytic cracking (FCC) is an important refinery process
by which heavy hydrocarbons are cracked to form lighter valuable products
over catalyst particles. FCC plants consist of the riser (reactor),
the regenerator, and the fractionator that separates the riser effluent
into the useful end products. In FCC plants the product specifications
and feedstocks change due to varying economic and market conditions.
In addition, FCC plants operate with large throughputs and a small
improvement realized by optimization and control yields significant
economic return. In previous work, we developed a nonlinear dynamic
model and validated it with industrial data. In this study, our focus
involves the development and application of a real-time optimization
framework. We propose a hierarchical structure which includes a two-layer
implementation of economic model predictive control (EMPC). EMPC provides
the optimal riser and the regenerator temperature reference trajectories
which are determined from a dynamic optimization problem maximizing
the plant profit. A regulatory model predictive controller (RMPC)
manipulates the catalyst circulation rate and the air flow rate to
track the reference trajectories provided by EMPC. We consider changes
in product prices and the feed content, both of which necessitate
online optimization. Dynamic simulations show that the proposed hierarchical
control structure achieves optimal tracking of plant profit during
transitions between different operating regimes thanks to the combined
efforts of EMPC and RMPC.
Artificial Neural Networks (ANNs) have been used in a wide range of applications for complex datasets with their flexible mathematical architecture. The flexibility is favored by the introduction of a higher number of connections and variables, in general. However, over-parameterization of the ANN equations and the existence of redundant input variables usually result in poor test performance. This paper proposes a superstructure-based mixed-integer nonlinear programming method for optimal structural design including neuron number selection, pruning, and input selection for multilayer perceptron (MLP) ANNs. In addition, this method uses statistical measures such as the parameter covariance matrix in order to increase the test performance while permitting reduced training performance. The suggested approach was implemented on two public hyperspectral datasets (with 10% and 50% sampling ratios), namely Indian Pines and Pavia University, for the classification problem. The test results revealed promising performances compared to the standard fully connected neural networks in terms of the estimated overall and individual class accuracies. With the application of the proposed superstructural optimization, fully connected networks were pruned by over 60% in terms of the total number of connections, resulting in an increase of 4% for the 10% sampling ratio and a 1% decrease for the 50% sampling ratio. Moreover, over 20% of the spectral bands in the Indian Pines data and 30% in the Pavia University data were found statistically insignificant, and they were thus removed from the MLP networks. As a result, the proposed method was found effective in optimizing the architectural design with high generalization capabilities, particularly for fewer numbers of samples. The analysis of the eliminated spectral bands revealed that the proposed algorithm mostly removed the bands adjacent to the pre-eliminated noisy bands and highly correlated bands carrying similar information.
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