Sequential Solution Strategy Research Articles

Global self-optimizing control with active-set changes: A polynomial chaos approach

Global self-optimizing control (gSOC) aims to identify optimal controlled variables (CVs) that minimize the average economic cost when uncertainties vary in the whole distribution space. Rigorous numerical optimization for the global optimal CVs is mainly hampered by the intensive computation load, hence only approximate solutions were previously developed to afford tractable computations. These approximations may however be large in many cases. This paper revisits this challenging problem within the nonlinear programming (NLP) framework for gSOC and proposes a sequential solution strategy. Within the solution method, the polynomial chaos expansion (PCE) is introduced for the sake of fast computations of the statistics of the cost function. We also handle the active-set change problem by satisfying chance constraints. To this end, PCEs of the constrained variables are also constructed, to formulate conditions that should be respected for the CVs. To determine the PCE coefficients, the sparse grid collocation method is adopted to further reduce the computation burden, as the dimension of uncertainty could be large for most gSOC problems. Three case studies are provided to show the new gSOC approach, all of which result in more accurate CVs, while maintaining tractable numerical optimizations.

A novel formulation and sequential solution strategy with time-space adaptive mesh refinement for efficient reconstruction of local boundary heat flux

Inverse heat conduction problems appear in a variety of applications in industry and academia. Due to their mathematical challenges, they have been studied extensively over the last decades. Nevertheless, the solution of three dimensional transient inverse heat conduction problems are still computationally expensive. Commonly used solution approaches include the regularization-based approaches such as Tikhonov regularization or iterative regularization that result in formulating and solving optimization problems. A radically different solution approach is presented in this paper to provide efficient solutions of three dimensional transient inverse heat conduction problems on thin-plates that are used very often in industrial applications. Instead of solving optimization problems subject to constraints given in terms of three dimensional partial differential equations, the suggested approach transforms the inverse problem into an easy-to-solve direct problem that only needs the reconstruction of a Dirichlet boundary condition. This yields an approximated solution. Furthermore, a new time-space adaptive mesh refinement strategy is proposed to further reduce computational effort at an acceptable level of estimation precision. The accuracy and efficiency of the proposed sequential approach as well as the time-space adaptive mesh refinement strategy are validated by four representative case studies arising from practice. Estimation results with experimental data are also presented. The current work is considered as an important step forward towards the efficient solution of transient three dimensional inverse heat conduction problems, which is particularly useful for developing heat-flux soft sensors in practical problems arising from different fields such as pool boiling, falling films and steelmaking.

Optimal Design of Heat-Integrated Water Allocation Networks

Industrial operations consume energy and water in large quantities without accounting for potential economic and environmental burdens on future generations. Consumption of energy (mainly in the form of high pressure steam) and water (in the form of process water and cooling water) are essential to all processes and are strongly correlated, which requires development of systematic methodologies to address their interconnectivity. To this end, the subject of heat-integrated water allocation network design has received considerable attention within the research community in recent decades while further growth is expected due to imposed national and global regulations within the context of sustainable development. The overall mathematical model of these networks has a mixed-integer nonlinear programming formulation. As discussed in this work, proposed models in the literature have two main difficulties dealing with heat–water specificities, which result in complex formulations. These difficulties are addressed in this work through proposition of a novel nonlinear hyperstructure and a sequential solution strategy. The solution strategy is to solve three sub-problems sequentially and iteratively generate a set of potential solutions through the implementation of integer cut constraints. The novel mathematical approach also lends itself to an additional innovation for proposing multiple solutions balancing various performance indicators. This is exemplified with both a literature test case and an industrial-scale problem. The proposed solutions address a variety of performance indicators which guides decision-makers toward selecting the most appropriate configuration(s) among a large number of potential possibilities. Results exhibit that despite having a sequential solution strategy, better performance can be reached compared to previous approaches with the additional benefit of providing many potential solutions for further consideration by decision-makers to select the best case-specific solution.

Sequential synthesis of heat integrated water networks: A new approach and its application to small and medium sized examples

This paper presents a new step-wise sequential solution strategy for the synthesis of heat integrated water networks (HIWNs) comprising of two mathematical models. The first model minimizes water and energy costs. The optimal freshwater and water flow rates within the HIWN are determined from this model. Using these optimal flow rates, different configurations of HIWN are evaluated for the purpose of heat integration. The second model is the stage-wise heat exchanger network (Yee and Grossmann, 1990), which is solved for each of the evaluated network configuration in a sequential manner. Using this proposed strategy, a set of locally optimal HIWNs are produced and the best one is chosen based on the minimum total annual cost (TAC). The proposed sequential strategy is applied to small and medium sized examples in the literature. The results show that the proposed new sequential solution strategy can be successfully applied to small and medium sized HIWN problems.

MINLP Formulation for Simultaneous Planning, Scheduling, and Control of Short-Period Single-Unit Processing Systems

A simultaneous strategy for solving the integrated planning, scheduling, and control problem considering short-term periods is proposed in this paper. The problem is formulated as a mixed integer dynamic optimization problem. The main practical motivation to use a simultaneous rather than a sequential solution strategy is to seek improved optimal solutions by considering the interactions among planning, scheduling, and control. Integration of the three levels of the problem represents a challenge given the very different horizon times involved in the operations, resulting in growth of the problem in terms of the number of equations to be solved and hence on computational requirements to carry it out. A full space approach was used rather than trying a decomposition strategy. Moreover, a nonlinear model predictive control strategy was also used to account for online product transition trajectories. The integrated planning, scheduling, and control is formulated as a mixed integer dynamic optimization model, which is tested using the dynamic models of three continuous stirred tank reactors featuring different nonlinear behavior.

Performance Analysis of Three Controllers for the Polymerisation of Styrene in a Batch Reactor

The performance analysis of three advanced non linear controllers is the main focus of this paper. All three controllers are applied for the control of a batch polymerisation reactor which is defined by a very simple kinetic model for the polymerisation of styrene. This simple set of equations describing the polymerisation process is first solved using the sequential strategy i.e. Control Vector Parameterisation (CVP) technique within gPROMS to find optimal initial initiator concentrations and the reactor temperature trajectory necessary to yield desired polymer molecular properties (defined here as fixed values of monomer conversion and number average chain length) in minimum time. The sequential solution strategy has had limited application in solving optimisation problems for polymerisation in batch reactors, most researchers instead employing the Pontryagin's Maximum Principle (PMP) to solve optimal control problems involving these systems.The temperature trajectory obtained from the dynamic optimisation is used as the setpoint to be tracked by the three controllers: Dual Mode control with PID, which is representative of industrial practice, Generic Model Control (GMC) with Neural Networks as online heat release estimator, and Direct Inverse Control (DIC). Published work on the last two controllers as applied to the control of a batch polymerisation reactor is absent from the literature.When the performances of the different controllers are evaluated, it is seen that the GMC-NN controller performs better than the other two for the system under consideration.

Parameter identification in constitutive models via optimization with a posteriori error control

AbstractIn this paper we outline a computational technique for the calibration of macroscopic constitutive laws with automatic error control. In the most general situation the state variables of the constitutive law, as well as the material parameters, are spatially non‐homogeneous. The experimental observations are given in space–time. Based on an appropriate dual problem, we compute a posteriori the discretization error contributions from approximations of the parameter, state and costate fields in space–time for an arbitrarily chosen goal‐oriented error measure of engineering significance. Such a measure can be used in an adaptive strategy (not discussed in this paper) to meet a predefined error tolerance. An important observation is that the Jacobian matrix associated with the resulting Newton method is used (in principle) in solving the dual problem. Rather than treating the Jacobian in a monolithic fashion, we utilize a sequential solution strategy, whereby the FE‐topology of the discretized state problem is used repeatedly. Moreover, the proposed solution strategy lends itself naturally to the computation of first and second order sensitivities, which are obtained with little extra computational effort. Numerical results are given for the prototype model of confined aquifer flow with spatially non‐homogeneous permeability. The efficiency of the optimization strategy and the effectivity of the error computation are assessed. Copyright © 2005 John Wiley & Sons, Ltd.