Real-time Optimization Applications Research Articles

Real‐Time Optimization Using Machine Learning Models Applied to the 4,4′‐Diphenylmethane Diisocyanate Production Process

AbstractIn this work, the optimal time‐varying allocation of steam in a large‐scale industrial isocyanate production process is addressed. This is a problem that falls into the category of real‐time optimization (RTO). The application of RTO in practice faces two problems: First the available rigorous process models may not be suitable for use in real‐time connected to the process. Second, there is always a mismatch between the predictions of the model and the behavior of the real plant. We address the first problem by training a neural net model as a surrogate to data generated by a rigorous simulation model so that the model is simple to implement and short execution times result. The second problem is tackled by adapting the optimization problem based on measured data such that convergence to the optimal operating conditions for the real plant is achieved.

Experimental Application of Real-Time Optimization with Modifier Adaptation and Quadratic Approximation to a Reactive Extrusion Process

In this contribution, Real-Time Optimization with Modifier Adaptation and Quadratic Approximation (MAWQA) is experimentally applied to a pilot-scale 18 mm reactive extruder for the production of hydrophobically modified ethoxylated urethanes which are used as rheological paint additives. Standard model-based control is in this application not applicable because of the complex coupling of the chemical reaction, complex internal flows within the equipment, and a high sensitivity to external disturbances. The optimization is performed with the goal to minimize the specific energy requirement for the product by changing the overall throughput and the barrel temperature locally while meeting a hard constraint on the product quality. The product quality is determined by the viscosity of the product which is measured online with a capillary viscometer. In contrast to other work, the MAWQA method is applied here purely data-based without using a physical model. Despite the absence of a rigorous model, the method converged to the optimum after 6 initial probing moves and 4 iterations where the product quality constraints were already met.

Exergy, Energy, Economic, and Environmental Assessment of Condensate Stabilization Unit Through Advanced Process Control: Application of Real-Time Optimization

Exergy, Energy, Economic, and Environmental Assessment of Condensate Stabilization Unit Through Advanced Process Control: Application of Real-Time Optimization

A Real-Time Optimization Strategy for Small-Scale Facilities and Implementation in a Gas Processing Unit

The rise of new digital technologies and their applications in several areas pushes the process industry to update its methodologies with more intensive use of mathematical models—commonly denoted as digital twins—and artificial intelligence (AI) approaches to continuously enhance operational efficiency. In this context, Real-time Optimization (RTO) is a strategy that is able to maximize an economic function while respecting the existing constraints, which enables keeping the operation at its optimum point even though the plant is subjected to nonlinear behavior and frequent disturbances. However, the investment related to the project of commercial RTOs may make its application infeasible for small-scale facilities. In this work, an in-house, small-scale RTO is presented and its successful application in a real industrial case—a Natural Gas Processing Unit—is shown. Besides that, a new method for enhancing the efficiency of using sequential-modular simulator inside an optimization framework and a new method to account for the economic return of optimization-based tools are proposed and described. The application of RTO in the industrial case showed an enhancement in the stability of the main variables and an increase in profit of 0.64% when compared to the operation of the regulatory control layer alone.

Real-time optimization strategy by using sequence quadratic programming with multivariate nonlinear regression for a fuel cell electric vehicle

The energy management of a plug-in FCEV (Fuel Cell Electric Vehicle) strictly depends on the control of SOC (State of Charge) over a given trip distance. The SOC may be varied with the trip distance by updating an EF (Equivalent Factor), which is derived from ECMS (Equivalent Consumption Minimization Strategy). However, the EF is too complicated to estimate accurately in real-time with traditional method. A real-time optimization strategy by using SQP (Sequence Quadratic Programming) with MNLR (Multivariate Nonlinear Regression) is proposed for a plug-in FCEV. First, the real-time hydrogen consumption optimization problem for SOC trip distance adaptive is formulated by using ECMS. The EF is adjusted according to the trip distances and predefined SOC. Then, in order to improve the accuracy of EF, SQP method is utilized to optimize the fuel cell and battery efficiency. Thus, the MNLR is applied to construct the fuel cell and battery efficiency response surface models for real-time optimization application. Finally, numerical verification and hardware in loop experiments are conducted to validate the proposed strategy. The results indicate that the combination of SQP with MNLR made it possible to develop the proposed strategy capable of significantly improving the hydrogen economic performance of this FCEV.

Real-time optimization of multi-cell industrial evaporative cooling towers using machine learning and particle swarm optimization

Existing electrical generating stations must operate with greater flexibility due to increasing renewable energy penetration on the electrical grid, and many coal-fired power stations have transitioned away from baseload operation to load-following operation to aid in grid stability. In cases where multiple independently controlled cooling tower cells are used in parallel for the cooling purposes of such stations, there is an opportunity to increase plant efficiency through data-driven optimization across their full load ranges. This work presents a novel application of real-time optimization using machine learning and particle swarm optimization on a multi-cell induced-draft cooling tower servicing a coal-fired power station under variable load. This is the first work to demonstrate simultaneous optimization of a multi-cell cooling tower, in addition to using machine learning for closed-loop control on a cooling tower. A novel control configuration is presented that ensures original control logic is not adversely affected and that the overall plant process is not disrupted using only existing hardware and operational data. To verify this methodology, the 12 independent cooling tower cells are simulated in parallel using historic operating data to demonstrate the effectiveness of real-time optimization compared to current practice. An artificial neural network is trained to predict overall cooling tower power consumption using only operational data and ambient conditions with an R2 value of greater than 0.96. The real-time optimization using particle swarm yields 6.7% annual energy usage savings compared to current practices, although the extent of the real-time savings varies greatly with both plant load and environmental conditions. This is particularly significant for a variable load situation because frequent ramping typically results in reduced overall efficiency. This proposed AI-based solution presents an opportunity to improve the overall heat rate of a load-following coal-fired power plant without the need to perform extensive first-principles modeling or add additional hardware to the cooling tower, resulting in more resources conserved and less overall emissions per unit of electricity generated.

Real-time optimization of an experimental solid-oxide fuel-cell system

There still exists a large gap between simulation work and industrial applications in the context of control and optimization of solid-oxide fuel-cell (SOFC) systems. In an effort to bridge this gap, this study describes the experimental implementation of steady-state real-time optimization (RTO) to an SOFC system that consists of both hardware and software components. The proposed adaptive optimization scheme uses an approximate steady-state model of the fuel-cell system and corrects it “appropriately” so that it becomes “excellent” for optimization. This way, the plant can be steered efficiently toward optimality, while meeting the varying electric power demand. In these experiments, the plant efficiency was increased from 55% to 62% through application of RTO. Furthermore, although the SOFC system is characterized by slow thermal dynamics that may take a few hours to settle to steady state, it has been possible to reduce the time necessary to reach the power setpoint from 1 h to about 5 min thanks to the use of transient measurements and a dynamic model. This experimental work has shown that it is possible, not only to control the SOFC system at a desired operating point, but also to operate it near optimality despite changes in power demand.

Dynamic optimization of a district energy system with storage using a novel mixed-integer quadratic programming algorithm

As more renewable energy is integrated into the power grid, it is increasingly important to exploit variable electricity pricing structures to minimize commercial utility costs and enable more intermittent renewables on the grid through proactive management of energy storage. Using data from a large campus district energy system, equipped with centralized chilled water plants and a thermal energy storage tank, a novel technique is proposed to optimize this system in real-time, formulated as a mixed-integer quadratic programming problem. This method, titled Quadratic Programming Hybrid with Augmented Constraints, is sufficiently fast to be computed in real-time for a district chiller system. This method is compared to both Branch and Bound and a simple logical decision algorithm in both speed and optimality. The proposed method for solving this mixed-integer quadratic programming problem proves very successful at achieving a near-optimal solution when compared to a standard Branch and Bound (BnB) algorithm. Although suboptimal, the proposed algorithm takes 99.96–99.99% less computational time than the standard BnB and computes an answer to within 29.9% of the BnB objective function. When compared to a simple logical decision algorithm, which represents an operator manually controlling the plant, the proposed method is estimated to yield 8.10–33.7% in savings on chiller energy costs. The Quadratic Programming Hybrid with Augmented Constraints algorithm shows potential for use in a real-time optimization application to exploit variable electricity pricing and significantly reduce the costs of running a chiller plant with thermal energy storage.

An Augmented Lagrangian Filter Method for Real-Time Embedded Optimization

We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal–dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and air conditioning system. Our numerical tests are performed on a standard processor and on an embedded platform. We demonstrate that the approach reduces solution times by a factor of over 1000.

Observers for Mass and Energy Balance Calculation in Metallurgical Plants

AbstractThe paper deals with observers for dynamic data reconciliation in mineral and metallurgical processing plants. In these industrial domains, improvement of data quality could have a significant impact on benefits generated by advanced control and real-time optimization applications. A review of the most common approaches is presented and the different observers are evaluated using benchmark plants. The aim of the paper is to compare the performance of methods in a systematic way and to highlight their strengths and weaknesses. For this purpose, a separation unit and a typical flotation circuit operating in stationary mode are used as benchmarks. Improvements to stationary observer that takes into account the autocovariance of accumulation rate is also proposed.

Real-time optimization using proper orthogonal decomposition: Free surface shape prediction due to underwater bubble dynamics

A new data-driven reduced-order modeling approach for real-time optimization applications is presented. The proper orthogonal decomposition (POD) technique is used for the reduced-order model, with the basis functions determined from an ensemble of offline high-fidelity simulations. For optimization in real time, a rapid two-stage approach is taken in the online phase: the POD coefficients are first determined by solving a small optimization problem, and the desired parameters are subsequently obtained by interpolation of the POD coefficients using precomputed information from the simulation ensemble. This method is applied to optimizing parameters for underwater bubble explosions so that a desired free surface shape is generated. For time-critical applications, such as using the water barrier generated to stop sea-skimming objects, the time available for online optimization is limited to about 30 s. Results for two-dimensional simulation, using a personal computer (dual CPU running at 2.8 GHz), show that our new methodology is able to meet such a critical time requirement. For three-dimensional simulations, the time taken for computation increases, and a faster computer or parallel implementation is required.

Constrained real-time optimization of a grinding circuit using steady-state linear programming supervisory control

This paper presents an application of real-time optimization (RTO) to a simulated ore grinding plant. The control and optimization methods are based on a dynamic linear model of the process. A linear programming (LP) method is used on-line to find the optimum controller set-point as a function of the process-operating constraints. The optimizer selects set-point values that maximize circuit throughput subject to constraints on circulating load, pump box level and hydrocyclone overflow and underflow densities. At the regulatory control level, performances of unconstrained and constrained multivariable predictive controllers are compared and discussed.