@misc{MappasVassiliadisDorneanuetal., author = {Mappas, Vassileios and Vassiliadis, Vassilios S. and Dorneanu, Bogdan and Arellano-Garc{\´i}a, Harvey}, title = {Maintenance scheduling optimisation of Reverse Osmosis Networks (RONs) via a multistage Optimal Control reformulation}, series = {Desalination}, volume = {543}, journal = {Desalination}, issn = {1873-4464}, doi = {10.1016/j.desal.2022.116105}, abstract = {State-of-the-art approaches for membrane cleaning scheduling have focused on the Mixed-Integer Nonlinear Programming (MINLP) formulation so far, a strategy leading to a combinatorial problem that does not capture accurately the dynamic behaviour of the system. In this work, the Reverse Osmosis (RO) cleaning scheduling problem is solved using a novel approach based on the Multistage Integer Nonlinear Optimal Control Problem (MSINOCP) formulation. The approach produces an automated solution for the membrane cleaning scheduling, which also obviates the need for any form of combinatorial optimisation. Two different simulations, for 26 and 52 periods of operation (each period with a duration of one week), are carried out to illustrate the application of the proposed framework and the total cost is 1.17 and 2.48 10⁷ €, respectively. The RO network configuration considers 2 stages, each with 3 individual RO modules. The results show evidently that the new proposed solution framework can solve successfully this type of problems, even for large scale configurations, long time horizons and arbitrary realistic complexity of the underlying dynamic model of the RO process considered.}, language = {en} } @misc{DorneanuMappasVassiliadisetal., author = {Dorneanu, Bogdan and Mappas, Vassileios and Vassiliadis, Vassilios S. and Arellano-Garc{\´i}a, Harvey}, title = {Novel parametric gradient calculation method for multistage systems with generalized constraints}, series = {2024 AIChE Annual Meeting}, journal = {2024 AIChE Annual Meeting}, pages = {3}, abstract = {Sensitivity and gradient evaluations are essential for understanding the variability of a system subject to changes in input parameters, aiding in applications such as optimization, control, or decision-making processes (Castillo et al., 2008; Logsdon and Biegler, 1989, Horn and Tsai, 1967). Various approaches are available for the gradient evaluation in the simulation of large-scale steady-state systems, utilizing techniques such as automatic differentiation, sensitivity analysis, optimization or machine learning (Amaran et al., 2016). The term large-scale refers to problems with a substantial number of design variables, structural state variables, or constraint functions, or a combination thereof, necessitating significant high-performance parallel computing resources to solve within a reasonable timeframe (Kennedy and Martins, 2014). However, the evaluation of gradients in large-scale multistage systems simulation poses significant challenges due to computational complexity, numerical instability, scalability issues, and the limitations of the traditional differentiation techniques. Additionally, model complexity, sensitivity to noise, and data requirements of machine learning-based approaches further amplify these challenges. Overcoming these obstacles necessitates the development of efficient, scalable and robust gradient evaluation techniques that can effectively handle the characteristics of large-scale systems while offering reliable insights for a wide array of applications. This contribution focuses on re-examining and advancing the evaluation of parametric sensitivities within the context of simulating highly complex, hierarchical multiscale modular systems of very large size. The models being analyzed may necessitate sensitivity evaluations concerning their response to parametric inputs. These evaluations serve not only to test and verify their robustness, but also to integrate them into modular structures within a comprehensive optimization framework. Such an optimization framework aims to enhance system performance based on selected criteria, while simultaneously adhering to essential optimality constraints. While gradient-free optimization methods have been successfully applied to important design problems, their applications typically involve no more than O(102) design variables, and these methods exhibit very poor scalability with the dimensionality of the design variables (Kennedy and Martins, 2014). For large-scale, high-fidelity applications, gradient-based methods are deemed more suitable, although the challenges related to computational time and accuracy need to be addressed. To address these challenges, the use of either sensitivities or appropriately generalized adjoint equations for efficient calculation of constraint and objective functions gradients for generalized multistage systems, irrespective of whether they are dynamic in nature or they are steady-state. The proposed approach adopts a generalized modular strategy suitable for any type of system, starting from a traditional sensitivity-based calculations initially, and subsequently developing a novel generalized adjoint-based method. The resulting algorithm comprises a sequence of forward and backward sweep computational steps, which are entirely equivalent, and serve as a generalization of the adjoint-based calculation methods for gradients of constraints. These methods find application in various numerical analysis computations related to dynamical systems, including optimal control problems. It has to be noted that the model is regarded as a general modular representation of any coupled system, without making a distinction between dynamic or steady-state systems. In this context, a dynamic system is perceived as having state profiles as private internal variables, while interacting with its external environment through the input of initial conditions and parameter values. Its output consists of final conditions or any internal trajectory points that require reporting to the external environment during dynamic simulation. The proposed strategy using a novel adjoint scheme generalizes this approach to any multistage system model, of which the stages need not be of dynamic nature, such as in the use of adjoint equations in optimal control of multistage Differential- Algebraic Equation (DAE) systems (Morison and Sargent, 1986). The choice between the use of the adjoint- and the sensitivity-based approach depends on the balance between the number of constraints/functions requiring gradient evaluation, and the number of states in the underlying dynamical system. The adjoint-based approach may be advantageous when dealing with a smaller number of constraints than state variables that require gradient evaluation, whereas the sensitivity-based approach could be more computationally efficient for a larger number of constraints than state variables in the modular treatment of the underlying dynamic system. The simulation of a multistage system is demonstrated using an example consisting of steady-state feedforward blocks, employing both the sensitivity- and the proposed adjoint-based approach. The results obtained reveal that the numerical values derived from the gradient evaluation are identical for both methods. Therefore, it can be concluded that the newly introduced approach for general multistage sequential systems is entirely non-restrictive. This indicates its effectiveness and applicability, offering flexibility and robustness in gradient evaluation for such systems.}, language = {en} } @misc{MappasDorneanuHeinzelmannetal., author = {Mappas, Vassileios and Dorneanu, Bogdan and Heinzelmann, Norbert and Schnitzlein, Klaus and Arellano-Garc{\´i}a, Harvey}, title = {A unified modular framework for modeling multiphase reactors}, series = {Annual Meeting of Process Engineering and Materials Technology 2024}, journal = {Annual Meeting of Process Engineering and Materials Technology 2024}, language = {en} } @misc{MappasDorneanuVassiliadisetal., author = {Mappas, Vassileios and Dorneanu, Bogdan and Vassiliadis, Vassilios S. and Arellano-Garc{\´i}a, Harvey}, title = {Multistage optimal control and nonlinear programming formulation for automated control loop selection}, series = {Computer Aided Chemical Engineering}, volume = {53}, journal = {Computer Aided Chemical Engineering}, issn = {1570-7946}, doi = {10.1016/B978-0-443-28824-1.50327-6}, pages = {1957 -- 1962}, abstract = {Control loop design, as well as controller tuning, constitute the pillars of process control to achieve design specifications and smooth process operation, and to meet predefined performance criteria. Currently, state-of-the-art approaches have focused on methods that yield only the pairings between input and output methods, and are not able to incorporate path and end-point constraints. This work introduces a novel strategy based on the multistage optimal control formulation of the control loop selection problem. This approach overcomes the drawbacks of traditional methods by producing an automated integrated solution for the task of control loop design. Furthermore, it obviates the need for any form of combinatorial optimization and incorporating path and terminal constraints. The results show that the proposed solution framework produces the same control loops as in the case of traditional approaches, however the inclusion of path and end-point constraints improves the performance of the control profiles.}, language = {en} } @misc{VassiliadisMappasEspaasetal., author = {Vassiliadis, Vassilios S. and Mappas, Vassileios and Espaas, Tomas A. and Dorneanu, Bogdan and Isafiade, Adeniyi and M{\"o}ller, Klaus and Arellano-Garc{\´i}a, Harvey}, title = {Reloading process systems engineering within chemical engineering}, series = {Chemical Engineering Research and Design}, volume = {209}, journal = {Chemical Engineering Research and Design}, doi = {10.1016/j.cherd.2024.07.066}, pages = {380 -- 398}, abstract = {Established as a sub-discipline of Chemical Engineering in the 1960s by the late Professor R.W.H. Sargent at Imperial College London, Process Systems Engineering (PSE) has played a significant role in advancing the field, positioning it as a leading engineering discipline in the contemporary technological landscape. Rooted in Applied Mathematics and Computing, PSE aligns with the key components driving advancements in our modern, information-centric era. Sargent's visionary foresight anticipated the evolution of early computational tools into fundamental elements for future technological and scientific breakthroughs, all while maintaining a central focus on Chemical Engineering. This paper aims to present concise and concrete ideas for propelling PSE into a new era of progress. The objective is twofold: to preserve PSE's extensive and diverse knowledge base and to reposition it more prominently within modern Chemical Engineering, while also establishing robust connections with other data-driven engineering and applied science domains that play important roles in industrial and technological advancements. Rather than merely reacting to contemporary challenges, this article seeks to proactively create opportunities to lead the future of Chemical Engineering across its vital contributions in education, research, technology transfer, and business creation, fully leveraging its inherent multidisciplinarity and versatile character.}, language = {en} } @misc{MappasVassiliadisDorneanuetal., author = {Mappas, Vassileios and Vassiliadis, Vassilios S. and Dorneanu, Bogdan and Arellano-Garc{\´i}a, Harvey}, title = {Use of Multistage Optimal Control Principles for Novel Design and Implementation of Classical Controllers}, series = {AIChE Annual Meeting}, journal = {AIChE Annual Meeting}, abstract = {Classical controllers, such as Proportional-Integral (PI) and Proportional-Integral Derivative (PID) controllers, are the most long-established and widely used in industry. Various methods for tuning these types of controllers exist (Ziegler et al., 1942; Blondin et al., 2018; Do et al., 2021), and up to this point, there is no fruitful avenue to improve their performance. In this contribution, a new approach for PI and PID controller implementation, based on a Multistage Optimal Control (MSOCP) approach is introduced. Our approach incorporates path and end-point constraints during its controller tuning phase, as well as parameter and disturbance uncertainty. The proposed framework is applied for different case studies and is able to reject any disturbances introduced to the examined systems, with or without uncertainty, satisfies end-point constraints and exhibits quicker response for switching steady states, compared to classical methods. Other aspects of controller design and incorporation within industrial process models, as related to using rigorous optimization methodologies and implementations, will further be highlighted within the context of the PI and PID controllers.}, language = {en} } @misc{MappasVassiliadisDorneanuetal., author = {Mappas, Vassileios and Vassiliadis, Vassilios S. and Dorneanu, Bogdan and Arellano-Garc{\´i}a, Harvey}, title = {Automated Control Loop Selection Via Multistage Optimal Control Formulation and Nonlinear Programming}, series = {Chemical Engineering Research and Design}, volume = {195}, journal = {Chemical Engineering Research and Design}, issn = {1744-3563}, doi = {10.1016/j.cherd.2023.05.041}, pages = {76 -- 95}, abstract = {In this work, a novel approach based on the multistage optimal control formulation of the control loop selection problem is introduced. Currently, state-of-the-art approaches for controller loop design have been focused on data that yield only the pairings between input-output variables, and are not able to incorporate path and end-point constraints. Thus, they only produce the optimal loops for control purposes, without the simultaneous consideration of their optimal tuning. This formulation overcomes these drawbacks by producing an automated integrated solution for the task of control loop design, which also obviates the need for any form of combinatorial optimisastion to be used. To illustrate the procedure, as well as the advantages of the proposed scheme, different practical case studies are discussed and the results compared with those obtained with standard controller loop selection methods and their tuning. The results of the proposed approach show improved performance over previous methodologies found in the literature. Furthermore, the framework is extended to the selection of the control loops that must obey path and end-point constraints imposed by the underlying dynamical process. This task is usually difficult for classical methods, which violate them or exhibit underdamped response in some cases.}, language = {en} } @misc{DorneanuMappasVassiliadisetal., author = {Dorneanu, Bogdan and Mappas, Vassileios and Vassiliadis, Vassilios S. and Arellano-Garc{\´i}a, Harvey}, title = {A second-order linesearch procedure within Newton's method for highly nonlinear steady-state systems simulation}, series = {2024 AIChE Annual Meeting}, journal = {2024 AIChE Annual Meeting}, abstract = {Linesearch, a crucial component of Newton's method, ensures global convergence, guaranteeing convergence to a local solution from any starting point while satisfying all simultaneous nonlinear equations (Bellavia and Morini, 2003). Despite Newton's method being considered established both theoretically and algorithmically, leaving little room for further improvements, this contribution focuses on enhancing the linesearch procedure and revealing significant advancements over existing methods. Specifically, this study aims to incorporate second-order information in a computationally efficient manner to improve the performance of the linesearch procedure, especially for highly nonlinear equation systems. Nonlinearity, particularly near the starting point, can substantially hinder algorithmic efficiency, necessitating frequent step reductions at the expense of function evaluations and major iterations involving Jacobian evaluations and factorizations (Gill and Zhang, 2024). The proposed approach leverages a a higher-order Taylor series expansion around the operating point of a major iteration in Newton's algorithm, coupled with a custom Jacobian vector product finite difference scheme. This combination requires only one additional Jacobian evaluation to construct a locally accurate fourth-degree polynomial approximating the merit function along the search direction. In addition to the theoretical advancements, this contribution provides computational evidence supporting the claim that for highly nonlinear systems, significant computational savings and enhanced solution procedure stability can be achieved. Utilizing a Python implementation, linear subsets of equations are treated separately to boost the efficiency of function and Jacobian evaluations, aligning with standard practices in professional software development. While Python may not be a high-performance language, its suitability for rapid algorithm prototyping and validation precedes potential transfer to higher-performance languages like C++. Moreover, given Newton's method central roles in various iterative solution tools, such as its repeated use within a Differential-Algebraic Equations (DAEs) integrators and potentially Partial Differential-Algebraic Equations (PDAEs) solvers, the significance of this work extends even further. Future research endeavors will explore these areas, building upon the foundations laid by this study.}, language = {en} }