168 results found
Peric N, Paulen R, Villanueva ME, et al., 2018, Set-membership nonlinear regression approach to parameter estimation, Journal of Process Control, Vol: 70, Pages: 80-95, ISSN: 0959-1524
This paper introducesset-membership nonlinear regression(SMR), a new approach to nonlinearregression under uncertainty. The problem is to determine the subregion in parameter spaceenclosing all (global) solutions to a nonlinear regression problem in the presence of boundeduncertainty on the observed variables. Our focus is on nonlinear algebraic models. We investigatethe connections of SMR with (i) the classical statistical inference methods, and (ii) the usual set-membership estimation approach where the model predictions are constrained within boundedmeasurement errors. We also develop a computational framework to describe tight enclosures ofthe SMR regions using semi-infinite programming and complete-search methods, in the form oflikelihood contour and polyhedral enclosures. The case study of a parameter estimation problemin microbial growth is presented to illustrate various theoretical and computational aspects of theSMR approach.
Pitt JA, Gomoescu L, Pantelides CC, et al., 2018, Critical assessment of parameter estimation methods in models of biological oscillators, IFAC-PapersOnLine, Vol: 51, Pages: 72-75, ISSN: 2405-8963
Many biological systems exhibit oscillations in relation to key physiological or cellular functions, such as circadian rhythms, mitosis and DNA synthesis. Mathematical modelling provides a powerful approach to analysing these biosystems. Applying parameter estimation methods to calibrate these models can prove a very challenging task in practice, due to the presence of local solutions, lack of identifiability, and risk of overfitting. This paper presents a comparison of three state-of-the-art methods: frequentist, Bayesian and set-membership estimation. We use the Fitzhugh-Nagumo model with synthetic data as a case study. The computational performance and robustness of these methods is discussed, with a particular focus on their predictive capability using cross-validation.
Graciano JEA, Chachuat B, Alves RMB, 2018, Conversion of CO2-Rich Natural Gas to Liquid Transportation Fuels via Trireforming and Fischer-Tropsch Synthesis: Model-Based Assessment, INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH, Vol: 57, Pages: 9964-9976, ISSN: 0888-5885
This paper presents a model-based analysis of a process coupling trireforming and Fischer–Tropsch technologies for the production of liquid fuels from CO2-rich natural gas. The process also includes an upgrading section based on hydrocracking, a separation section, a water gas shift unit, and a Rankine cycle unit for recovering the excess thermal energy produced by the Fischer–Tropsch reactor. Simulations are carried out in the process simulator Aspen Plus using standard unit operation models where applicable, while modeling the nonconventional units, such as the Fischer–Tropsch and hydrocracking reactors, using Aspen Custom Modeler. The proposed process could achieve a carbon conversion efficiency upward of 50% in the analyzed scenario, despite a natural gas feedstock with 30 mol % CO2. The analysis also reveals that the plant-wide electricity consumption could be covered nearly entirely by the Rankine cycle unit, enabling significant cost savings alongside a reduction of the overall global warming potential by about 10% in this specific case study. Finally, the results of a detailed economic assessment indicate that cheap natural gas is a prerequisite to the economic viability of the process, which would remain attractive in the current US scenario, yet presents a major impediment for its deployment in Brazil.
Quek V, Shah N, Chachuat B, 2018, Modeling for design and operation of high-pressure membrane contactors in natural gas sweetening, Chemical Engineering Research and Design, Vol: 132, Pages: 1005-1019, ISSN: 1744-3598
Over the past decade, membrane contactors (MBC) for CO2 absorption have been widely recognized for their large intensification potential compared to conventional absorption towers. MBC technology uses microporous hollow-fiber membranes to enable effective gas and liquid mass transfer, without the two phases dispersing into each other. The main contribution of this paper is the development and verification of a predictive mathematical model of high-pressure MBC for natural gas sweetening applications, based on which model-based parametric analysis and optimization can be conducted. The model builds upon insight from previous modeling studies by combining 1-d and 2-d mass-balance equations to predict the CO2 absorption flux, whereby the degree of membrane wetting itself is calculated from the knowledge of the membrane pore-size distribution. The predictive capability of the model is tested for both lab-scale and pilot-scale MBC modules, showing a close agreement of the predictions with measured CO2 absorption fluxes at various gas and liquid flowrates, subject to a temperature correction to account for the heat of reaction in the liquid phase. The results of a model-based analysis confirm the advantages of pressurized MBC operation in terms of CO2 removal efficiency. Finally, a comparison between vertical and horizontal modes of operation shows that the CO2 removal efficiency in the latter can be vastly superior as it is not subject to the liquid static head and remediation strategies are discussed.
Chachuat B, Sager S, 2018, Introduction to the Special Issue on Global and Robust Optimization of Dynamic Systems, Optimal Control Applications and Methods, Vol: 39, Pages: 425-426, ISSN: 0143-2087
Graciano JEA, Giudici R, Alves RMB, et al., 2018, A simple PLS-based approach for the construction of compact surrogate models, Computer Aided Chemical Engineering, Pages: 421-426
© 2018 Elsevier B.V. This work describes a simple algorithm based on partial least square (PLS) to enable the construction of surrogate models using a single tuning parameter. The proposed algorithm is illustrated with the case study of a membrane module for natural gas sweetening, where a mechanistic model is used as data generator. The effect of the tuning parameter is analysed, and it is shown that this parameter captures the trade-off between the surrogates’ accuracy and their complexity (number of terms). The algorithm performance is also compared with four different approaches from the literature, showing a similar performance.
Graciano JEA, Alves RMB, Chachuat B, 2018, Surrogate-based Optimization Approach to Membrane Network Synthesis in Gas Separation, Editors: Friedl, Klemes, Radl, Varbanov, Wallek, Publisher: ELSEVIER SCIENCE BV, Pages: 597-602
Peric ND, Villanueva ME, Chachuat B, 2017, Sensitivity analysis of uncertain dynamic systems using set-valued integration, SIAM Journal on Scientific Computing, Vol: 39, Pages: A3014-A3039, ISSN: 1064-8275
We present an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ordinary differential equation (ODE) systems, using both the forward and adjoint methods. The focus is on continuous-time set-valued integration, whereby auxiliary ODE systems are derived whose solutions describe high-order inclusions of the parametric trajectories in the form of polynomial models. The forward and adjoint auxiliary ODE systems treat the parameterization error of the original differential variables as a time-varying uncertainty, and propagate the sensitivity bounds forward and backward in time, respectively. This construction enables building on the sensitivity analysis capabilities of state-of-the-art solvers, such as CVODES in the SUNDIALS suite. Several numerical case studies are presented to assess the performance and accuracy of these set-valued sensitivity integrators.
Feng X, Villanueva ME, Chachuat B, et al., 2017, Branch-and-Lift algorithm for obstacle avoidance control, IEEE 56th Annual Conference on Decision and Control (CDC), Publisher: IEEE, ISSN: 0743-1546
Obstacle avoidance problems are a class of non-convex optimal control problems for which derivative-based optimization algorithms often fail to locate global minima. The goal of this paper is to provide a tutorial on how to apply Branch & Lift algorithms, a novel class of global optimal control methods, for solving such obstacle avoidance problems to global optimality. The focus of the technical developments is on how Branch & Lift methods can exploit the particular structure of Dubin models, which can be used to model a variety of practical obstacle avoidance problems. The global convergence properties of Branch & Lift in the context of obstacle avoidance is discussed from a theoretical as well as a practical perspective by applying it to a tutorial example.
Bernardi A, Nikolaou A, Meneghesso A, et al., 2017, Semi-empirical modeling of microalgae photosynthesis in different acclimation states - Application to N. gaditana., Journal of Biotechnology, Vol: 259, Pages: 63-72, ISSN: 0168-1656
The development of mathematical models capable of accurate predictions of the photosynthetic productivity of microalgae under variable light conditions is paramount to the development of large-scale production systems. The process of photoacclimation is particularly important in outdoor cultivation systems, whereby seasonal variation of the light irradiance can greatly influence microalgae growth. This paper presents a dynamic model that captures the effect of photoacclimation on the photosynthetic production. It builds upon an existing semi-empirical model describing the processes of photoproduction, photoregulation and photoinhibition via the introduction of acclimation rules for key parameters. The model is calibrated against a dataset comprising pulsed amplitude modulation fluorescence, photosynthesis rate, and antenna size measurements for the microalga Nannochloropsis gaditana in several acclimation states. It is shown that the calibrated model is capable of accurate predictions of fluorescence and respirometry data, both in interpolation and in extrapolation.
Puchongkawarin C, Vaupel Y, Guo M, et al., 2017, Towards the synthesis of wastewater recovery facilities using enviroeconomic optimization, The Water-Food-Energy Nexus - Processes, Technologies, and Challenges, Editors: Mujtaba, Srinivasan, Elbashir, ISBN: 9781498760843
The wastewater treatment industry is undergoing a major shift towards a proactive interest in recovering materials and energy from wastewater streams, driven by both economic incentives and environmental sustainability. With the array of available treatment technologies and recovery options growing steadily, systematic approaches to determining the inherent trade-off between multiple economic and environmental objectives become necessary, namely enviroeconomic optimization.The main objective of this chapter is to present one such methodology based on superstructure modeling and multi-objective optimization, where the main environmental impacts are quantified using life cycle assessment (LCA). This methodology is illustrated with the case study of a municipal wastewater treatment facility. The results show that accounting for LCA considerations early on in the synthesis problem may lead to dramatic changes in the optimal process configuration, therebysupporting LCA integration into decision-making tools for wastewater treatment alongside economical selection criteria.
Sun M, Villanueva ME, Pistikopoulos EN, et al., 2017, Robust multi-parametric control of continuous-time linear dynamic systems, IFAC-PapersOnLine, Vol: 50, Pages: 4660-4665, ISSN: 2405-8963
We extend a recent methodology called multi-parametric NCO-tracking for the design of parametric controllers for continuous-time linear dynamic systems in the presence of uncertainty The approach involves backing-off the path and terminal state constraints based on a worst-case uncertainty propagation determined using either interval analysis or ellipsoidal calculus. We address the case of additive uncertainty and we discuss approaches to handling multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservatism. These developments are illustrated with the case study of a fluidized catalytic cracking (FCC) unit operated in partial combustion mode.
Villanueva ME, Li JC, Feng X, et al., 2017, Computing ellipsoidal robust forward invariant tubes for nonlinear MPC, IFAC-PapersOnLine, Vol: 50, Pages: 7175-7180, ISSN: 2405-8963
Min-max differential inequalities (DIs) can be used to characterize robust forward invariant tubes with convex cross-section for a large class of nonlinear control systems. The advantage of using set-propagation over other existing approaches for tube MPC is that they avoid the discretization of control policies. Instead, the conservatism of min-max DIs in tube MPC arises from the discretization of sets in the state-space, while the control law is never discretized and remains defined implicitly via the solution of a min-max optimization problem. The contribution of this paper is the development of a practical implementation of min-max DIs for tube MPC using ellipsoidal-tube enclosures. We illustrate these developments with a spring-mass-damper system.
Houska B, Li JC, Chachuat B, 2017, Towards rigorous robust optimal control via generalized high-order moment expansion, Optimal Control Applications & Methods, Vol: 39, Pages: 489-502, ISSN: 1099-1514
This paper is concerned with the rigorous solution of worst-case robust optimal control problems havingbounded time-varying uncertainty and nonlinear dynamics with affine uncertainty dependence. We proposean algorithm that combines existing uncertainty set-propagation and moment-expansion approaches.Specifically, we consider a high-order moment expansion of the time-varying uncertainty, and we bound theeffect of the infinite-dimensional remainder term on the system state, in a rigorous manner, using ellipsoidalcalculus. We prove that the error introduced by the expansion converges to zero as more moments are added.Moreover, we describe a methodology to construct a conservative, yet more computationally tractable, robustoptimization problem, whose solution values are also shown to converge to those of the original robustoptimal control problem. We illustrate the applicability and accuracy of this approach with the robust time-optimal control of a motorized robot arm.
This paper is concerned with tube-based model predictive control (MPC) for both linear and nonlinear, input-affine continuous-time dynamic systems that are affected by time-varying disturbances. We derivea min-max differential inequality describing the support function of positive robust forward invariant tubes, which can be used to construct a variety of tube-based model predictive controllers. These constructions are conservative, but computationally tractable and their complexity scales linearly with the length of the prediction horizon. In contrast to many existing tube-based MPC implementations, the proposed framework does not involve discretizing the control policy and, therefore, the conservatism of the predicted tube depends solely on the accuracy of the set parameterization. The proposed approach is then used to construct a robustMPCscheme based on tubes with ellipsoidal cross-sections. This ellipsoidal MPC scheme is based on solving an optimal control problem under linear matrix inequality constraints. We illustrate these results with the numerical case study of a spring-mass-damper system.
Nikolaou A, Booth P, Gordon F, et al., 2017, Multi-physics modeling of light-limited microalgae growth in raceway ponds, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol: 49, Pages: 324-329, ISSN: 1474-6670
This paper presents a multi-physics modeling methodology for the quantitative prediction of microalgae productivity in raceway ponds by combining a semi-mechanistic model of microalgae growth describing photoregulation, photoinhibition and photoacclimation, with models of imperfect mixing based on Lagrangian particle-tracking and heterogeneous light distribution. The photosynthetic processes of photoproduction, photoregulation and photoinhibition are represented by a model of chlorophyll fluorescence developed by Nikolaou et al. (2015), which is extended to encompass photoacclimation. The flow is simulated with the commercial CFD package ANSYS, whereas light attenuation is described by the Beer-Lambert law as a first approximation. Full-scale simulation results are presented on extended time horizons. Comparisons are made in terms of areal productivities under both imperfect and idealized (CSTR) mixing conditions, and for various extraction rates and water depths.
Diaz-Bejarano E, Porsin AV, Macchietto S, et al., 2017, Fossil fuel: Energy efficient thermal retrofit options for crude oil transport in pipelines, The Water-Food-Energy Nexus: Processes, Technologies, and Challenges, Pages: 277-296, ISBN: 9781498760836
© 2018 by Taylor & Francis Group, LLC. Pipelines are used to transport large amounts of crude oil over large distances (either overland or subsea), representing the most economical alternative. Flow assurance faces two main problems: viscosity increase due to gradual cooling of the oil along the pipeline and fouling deposition. These problems are especially important in very cold environments (Russia, Alaska, North Sea, deep oceanic waters, etc.) and when dealing with nonconventional oils, usually heavy or extra-heavy oil and waxy oils. In many cases, the depletion of deposits in conventional oil reservoirs is gradually leading to more extraction of these types of feedstock from remote locations. All these situations result in pipeline transport difficulties such as increased pumping costs, reduced flow rates, and the possibility of flow inhibition or blockage, with potentially major economic impact (Correra et al., 2007; Martínez-Palou et al., 2011).
Rajyaguru J, Villanueva ME, Houska B, et al., 2016, Chebyshev model arithmetic for factorable functions, Journal of Global Optimization, Vol: 68, Pages: 413-438, ISSN: 1573-2916
This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden.
Baroukh C, Steyer JP, Bernard O, et al., 2016, dynamic Flux Balance Analysis of the Metabolism of Microalgae under a Diurnal Light Cycle, 11th IFAC Symposium on Dynamics and Control of Process Systems including Biosystems, Publisher: Elsevier, Pages: 791-796, ISSN: 1474-6670
Microalgae have received much attention in the context of renewable fuel production, due to their ability to produce in high quantities carbon storage molecules such as lipids and carbohydrates. Despite significant research effort over the last decade, the production yields remain low and need to be optimized. For that, a thorough understanding of carbon storage metabolism is necessary. This paper develops a constrained metabolic model based on the dFBA framework to represent the dynamics of carbon storage in microalgae under a diurnal light cycle. The main assumption here is that microalgae adapt their metabolism in order to optimize their production of functional biomass (proteins, membrane lipids, DNA, RNA) over a diurnal cycle. A generic metabolic network comprised of 160 reactions representing the main carbon and nitrogen pathways of microalgae is used to characterize the metabolism. The optimization problem is simplified by exploiting the right kernel of the stoichiometric matrix, and transformed into a linear program by discretizing the differential equations using a classical collocation technique. Several constraints are investigated. The results suggest that the experimentally observed strategy of accumulation of carbon storage molecules during the day, followed by their depletion during the night may indeed be the optimal one. However, a constraint on the maximal synthesis rate of functional biomass must be added for consistency with the biological observations.
Bernardi A, Nikolaou A, Meneghesso A, et al., 2016, Correction: High-Fidelity Modelling Methodology of Light-Limited Photosynthetic Production in Microalgae., PLOS One, Vol: 11, ISSN: 1932-6203
[This corrects the article DOI: 10.1371/journal.pone.0152387.].
Sun M, Chachuat B, Pistikopoulos EN, 2016, Design of multi-parametric NCO tracking controllers for linear dynamic systems, Computers and Chemical Engineering, Vol: 92, Pages: 64-77, ISSN: 1873-4375
A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a reduction in the number of critical regions. It calls for the solution of more difficult parametric optimization problems with linear differential equations embedded, whose critical regions are potentially nonconvex. Examples of constrained linear quadratic optimal control problems with parametric uncertainty are presented to illustrate the approach.
Nikolaou A, Bernardi A, Meneghesso A, et al., 2016, High-Fidelity Modelling Methodology of Light-Limited Photosynthetic Production in Microalgae, PLOS One, Vol: 11, ISSN: 1932-6203
Reliable quantitative description of light-limited growth in microalgae is key to improving the design and operation of industrial production systems. This article shows how the capability to predict photosynthetic processes can benefit from a synergy between mathematical modelling and lab-scale experiments using systematic design of experiment techniques. A model of chlorophyll fluorescence developed by the authors [Nikolaou et al., J Biotechnol 194:91–99, 2015] is used as starting point, whereby the representation of non-photochemical-quenching (NPQ) process is refined for biological consistency. This model spans multiple time scales ranging from milliseconds to hours, thus calling for a combination of various experimental techniques in order to arrive at a sufficiently rich data set and determine statistically meaningful estimates for the model parameters. The methodology is demonstrated for the microalga Nannochloropsis gaditana by combining pulse amplitude modulation (PAM) fluorescence, photosynthesis rate and antenna size measurements. The results show that the calibrated model is capable of accurate quantitative predictions under a wide range of transient light conditions. Moreover, this work provides an experimental validation of the link between fluorescence and photosynthesis-irradiance (PI) curves which had been theoricized.
Bernard O, Mairet F, Chachuat B, 2016, Modelling of Microalgae Culture Systems with Applications to Control and Optimization, Editors: Posten, Chen, Publisher: SPRINGER-VERLAG BERLIN, Pages: 59-87
Mathematical modeling is becoming ever more important to assess the potential, guide the design, and enable the efficient operation and control of industrial-scale microalgae culture systems (MCS). The development of overall, inherently multiphysics, models involves coupling separate submodels of (i) the intrinsic biological properties, including growth, decay, and biosynthesis as well as the effect of light and temperature on these processes, and (ii) the physical properties, such as the hydrodynamics, light attenuation, and temperature in the culture medium. When considering high-density microalgae culture, in particular, the coupling between biology and physics becomes critical. This chapter reviews existing models, with a particular focus on the Droop model, which is a precursor model, and it highlights the structure common to many microalgae growth models. It summarizes the main developments and difficulties towards multiphysics models of MCS as well as applications of these models for monitoring, control, and optimization purposes.
Ulmasov D, Baroukh C, Chachuat B, et al., 2016, Bayesian Optimization with Dimension Scheduling: Application to Biological Systems, Publisher: ELSEVIER SCIENCE BV
Adi VSK, Cook M, Peeva LG, et al., 2016, Optimization of OSN Membrane Cascades for Separating Organic Mixtures, Editors: Kravanja, Bogataj, Publisher: ELSEVIER SCIENCE BV, Pages: 379-384
Faust JMM, Fu J, Chachuat B, et al., 2016, Optimization of dynamic systems with rigorous path constraint satisfaction, Editors: Kravanja, Bogataj, Publisher: ELSEVIER SCIENCE BV, Pages: 643-648
Peric ND, Villanueva ME, Chachuat B, 2016, Set-valued integration of uncertain dynamic systems with sensitivity analysis capability, Editors: Kravanja, Bogataj, Publisher: ELSEVIER SCIENCE BV, Pages: 1165-1170
Sun M, Villanueva ME, Chachuat B, et al., 2016, Strategies towards the robust multi-parametric control of continuous-time systems, Pages: 355-357
Puchongkawarin C, Gomez-Mont C, Stuckey DC, et al., 2015, Optimization-based methodology for the development of wastewater facilities for energy and nutrient recovery, CHEMOSPHERE, Vol: 140, Pages: 150-158, ISSN: 0045-6535
Nikolaou A, Hartmann P, Sciandra A, et al., 2015, Dynamic coupling of photoacclimation and photoinhibition in a model of microalgae growth., Journal of Theoretical Biology, Vol: 390, Pages: 61-72, ISSN: 1095-8541
The development of mathematical models that can predict photosynthetic productivity of microalgae under transient conditions is crucial for enhancing large-scale industrial culturing systems. Particularly important in outdoor culture systems, where the light irradiance varies greatly, are the processes of photoinhibition and photoacclimation, which can affect photoproduction significantly. The former is caused by an excess of light and occurs on a fast time scale of minutes, whereas the latter results from the adjustment of the light harvesting capacity to the incoming irradiance and takes place on a slow time scale of days. In this paper, we develop a dynamic model of microalgae growth that simultaneously accounts for the processes of photoinhibition and photoacclimation, thereby spanning multiple time scales. The properties of the model are analyzed in connection to PI-response curves, under a quasi steady-state assumption for the slow processes and by neglecting the fast dynamics. For validation purposes, the model is calibrated and compared against multiple experimental data sets from the literature for several species. The results show that the model can describe the difference in photosynthetic unit acclimation strategies between Dunaliella tertiolecta (n-strategy) and Skeletonema costatum (s-strategy).
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