Joakim Beck - Academia.edu (original) (raw)

Papers by Joakim Beck

Computers & Chemical Engineering, 2015

Vacuum/pressure swing adsorption (VPSA) may be an attractive alternative to other separation proc... more Vacuum/pressure swing adsorption (VPSA) may be an attractive alternative to other separation processes for some applications. In particular, VPSA may be more energy efficient. However, there is often a trade-off between the different objectives in the separation: product purity, product recovery and power consumption. Identifying those trade-offs is possible through use of multi-objective optimisation methods. The use of multi-objective optimisation for the generation of a trade-off curve or surface is computationally challenging due to the size of the search space and the need for high fidelity simulations of the VPSA designs. The latter is necessary due to the inherently dynamic nature of the process. This paper presents the use of surrogate modelling to address the computational requirements of the high fidelity simulations needed to evaluate alternative designs. Surrogate modelling is an approach for defining simpler, lower fidelity models that capture the key behaviour of the high fidelity model that is necessary to select between alternative designs. We present SbNSGA-II ALM, surrogate based NSGA-II. It is a robust and fast multi-objective optimisation method based on kriging surrogate models and NSGA-II with Active Learning MacKay (ALM) design criteria. The SbNSGA-II ALM method is faster than the NSGA-II method while preserving the robustness and diversity of the Pareto front identified. The properties and capabilities of the SbNSGA-II ALM method are evaluated through the application to an industrially relevant cases study. Specifically, we consider a two column six step VPSA system for CO 2 /N 2 separation. Using the surrogate modelling approach, we observe a 5 times reduction in the number of high-fidelity VPSA simulations required, when compared with NSGA-II applied directly to the high fidelity model, to generate a similar Pareto front. The surrogate based multi-objective optimisation method may enable the comprehensive optimisation of adsorption based separation processes. This could lead to more efficient separations for applications ranging from carbon capture to portable oxygen concentrators.

Chemometrics and Intelligent Laboratory Systems, 2015

Optimization based process design tools are most useful when combined with the human engineer's i... more Optimization based process design tools are most useful when combined with the human engineer's insight. Further insight can be gained through the use of these tools by encouraging the exploration of the design space. Visualization is one technique which makes it easier for an engineer to understand the designs identified by an optimization tool. There are many visualization techniques but most are for individual process designs or for understanding the behavior a design space when a single design objective is considered. Most design problems, however, are multi-objective. This paper presents a multi-objective visualization method and applies it to the industrially relevant design of pressure swing adsorption systems.

ESAIM: Proceedings, 2011

In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elli... more In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product.

ABSTRACT This paper describes the testing, comparison and application of global sensitivity techn... more ABSTRACT This paper describes the testing, comparison and application of global sensitivity techniques for the study of the impact of the stream impurities on CO2 pipeline failure. Global sensitivity analysis through non-intrusive generalised polynomial chaos expansion with sparse grids is compared to more common techniques and is found to achieve superior convergence rate to crude Monte Carlo, quasi-Monte Carlo and EFAST for functions with up to a moderate level of “roughness”. This methodology is then applied to the hypothetical full bore rupture of a 1 km CO2 pipeline at 150 bara and 283.15 K. The sensitivity of the ensuing outflow to the composition of a quaternary mixture of CO2 with N2, CH4 and O2 as representative stream impurities. The results indicate that the outflow rate is highly sensitive to the composition during the early stages of depressurisation, where the effect of the impurities on phase equilibria has a significant impact on the outflow.

Lecture Notes in Computational Science and Engineering, 2013

In this work we explore the extension of the quasi-optimal sparse grids method proposed in our pr... more In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work "On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its effectiveness on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and an efficient nested quadrature rule with respect to the Gaussian weight.

Computer Aided Chemical Engineering, 2012

Pressure swing adsorption (PSA) is a cyclic adsorption process for gas separation and purificatio... more Pressure swing adsorption (PSA) is a cyclic adsorption process for gas separation and purification. PSA offers a broad range of design possibilities influencing the device behaviour. In the last decade much attention has been devoted towards simulation and optimisation of various PSA cycles. The PSA beds are modelled with hyperbolic/parabolic partial differential algebraic equations and the separation performance should be assessed at cyclic steady state (CSS). Detailed mathematical models together with the CSS constraint makes design difficult. We propose a surrogate based optimisation procedure based on kriging for the design of PSA systems. The numerical implementation is tested with a genetic algorithm, with a multi-start sequential quadratic programming method and with an efficient global optimisation algorithm. The case study is the design of a dual piston PSA system for the separation of a binary gas mixture of N 2 and CO 2 .

Mathematical Models and Methods in Applied Sciences, 2012

Computers & Mathematics with Applications, 2014

ABSTRACT In this work we consider quasi-optimal versions of the Stochastic Galerkin method for so... more ABSTRACT In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number NN of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CNCN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates.

Computer simulators can be computationally intensive to run over a large number of input values, ... more Computer simulators can be computationally intensive to run over a large number of input values, as required for optimization and various uncertainty quantification tasks. The standard paradigm for the design and analysis of computer experiments is to employ Gaussian random fields to model computer simulators. Gaussian process models are trained on input-output data obtained from simulation runs at various input values. Following this approach, we propose a sequential design algorithm, MICE (Mutual Information for Computer Experiments), that adaptively selects the input values at which to run the computer simulator, in order to maximize the expected information gain (mutual information) over the input space. The superior computational efficiency of the MICE algorithm compared to other algorithms is demonstrated by test functions, and a tsunami simulator with overall gains of up to 20% in that case.

Computers & Chemical Engineering, 2015

Vacuum/pressure swing adsorption (VPSA) may be an attractive alternative to other separation proc... more Vacuum/pressure swing adsorption (VPSA) may be an attractive alternative to other separation processes for some applications. In particular, VPSA may be more energy efficient. However, there is often a trade-off between the different objectives in the separation: product purity, product recovery and power consumption. Identifying those trade-offs is possible through use of multi-objective optimisation methods. The use of multi-objective optimisation for the generation of a trade-off curve or surface is computationally challenging due to the size of the search space and the need for high fidelity simulations of the VPSA designs. The latter is necessary due to the inherently dynamic nature of the process. This paper presents the use of surrogate modelling to address the computational requirements of the high fidelity simulations needed to evaluate alternative designs. Surrogate modelling is an approach for defining simpler, lower fidelity models that capture the key behaviour of the high fidelity model that is necessary to select between alternative designs. We present SbNSGA-II ALM, surrogate based NSGA-II. It is a robust and fast multi-objective optimisation method based on kriging surrogate models and NSGA-II with Active Learning MacKay (ALM) design criteria. The SbNSGA-II ALM method is faster than the NSGA-II method while preserving the robustness and diversity of the Pareto front identified. The properties and capabilities of the SbNSGA-II ALM method are evaluated through the application to an industrially relevant cases study. Specifically, we consider a two column six step VPSA system for CO 2 /N 2 separation. Using the surrogate modelling approach, we observe a 5 times reduction in the number of high-fidelity VPSA simulations required, when compared with NSGA-II applied directly to the high fidelity model, to generate a similar Pareto front. The surrogate based multi-objective optimisation method may enable the comprehensive optimisation of adsorption based separation processes. This could lead to more efficient separations for applications ranging from carbon capture to portable oxygen concentrators.

Chemometrics and Intelligent Laboratory Systems, 2015

Optimization based process design tools are most useful when combined with the human engineer's i... more Optimization based process design tools are most useful when combined with the human engineer's insight. Further insight can be gained through the use of these tools by encouraging the exploration of the design space. Visualization is one technique which makes it easier for an engineer to understand the designs identified by an optimization tool. There are many visualization techniques but most are for individual process designs or for understanding the behavior a design space when a single design objective is considered. Most design problems, however, are multi-objective. This paper presents a multi-objective visualization method and applies it to the industrially relevant design of pressure swing adsorption systems.

ESAIM: Proceedings, 2011

In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elli... more In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence of polynomial subspaces that features better convergence properties compared to standard polynomial subspaces such as Total Degree or Tensor Product.

ABSTRACT This paper describes the testing, comparison and application of global sensitivity techn... more ABSTRACT This paper describes the testing, comparison and application of global sensitivity techniques for the study of the impact of the stream impurities on CO2 pipeline failure. Global sensitivity analysis through non-intrusive generalised polynomial chaos expansion with sparse grids is compared to more common techniques and is found to achieve superior convergence rate to crude Monte Carlo, quasi-Monte Carlo and EFAST for functions with up to a moderate level of “roughness”. This methodology is then applied to the hypothetical full bore rupture of a 1 km CO2 pipeline at 150 bara and 283.15 K. The sensitivity of the ensuing outflow to the composition of a quaternary mixture of CO2 with N2, CH4 and O2 as representative stream impurities. The results indicate that the outflow rate is highly sensitive to the composition during the early stages of depressurisation, where the effect of the impurities on phase equilibria has a significant impact on the outflow.

Lecture Notes in Computational Science and Engineering, 2013

In this work we explore the extension of the quasi-optimal sparse grids method proposed in our pr... more In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work "On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construction of such quasi-optimal grid and show its effectiveness on a numerical example. In this approach, the two main ingredients are an estimate of the decay of the Hermite coefficients of the solution and an efficient nested quadrature rule with respect to the Gaussian weight.

Computer Aided Chemical Engineering, 2012

Pressure swing adsorption (PSA) is a cyclic adsorption process for gas separation and purificatio... more Pressure swing adsorption (PSA) is a cyclic adsorption process for gas separation and purification. PSA offers a broad range of design possibilities influencing the device behaviour. In the last decade much attention has been devoted towards simulation and optimisation of various PSA cycles. The PSA beds are modelled with hyperbolic/parabolic partial differential algebraic equations and the separation performance should be assessed at cyclic steady state (CSS). Detailed mathematical models together with the CSS constraint makes design difficult. We propose a surrogate based optimisation procedure based on kriging for the design of PSA systems. The numerical implementation is tested with a genetic algorithm, with a multi-start sequential quadratic programming method and with an efficient global optimisation algorithm. The case study is the design of a dual piston PSA system for the separation of a binary gas mixture of N 2 and CO 2 .

Mathematical Models and Methods in Applied Sciences, 2012

Computers & Mathematics with Applications, 2014

ABSTRACT In this work we consider quasi-optimal versions of the Stochastic Galerkin method for so... more ABSTRACT In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number NN of random inputs and an analytic dependence of the solution of the PDE with respect to the parameters in a polydisc of the complex plane CNCN. We show that a quasi-optimal approximation is given by a Galerkin projection on a weighted (anisotropic) total degree space and prove a (sub)exponential convergence rate. As a specific application we consider a thermal conduction problem with non-overlapping inclusions of random conductivity. Numerical results show the sharpness of our estimates.

Computer simulators can be computationally intensive to run over a large number of input values, ... more Computer simulators can be computationally intensive to run over a large number of input values, as required for optimization and various uncertainty quantification tasks. The standard paradigm for the design and analysis of computer experiments is to employ Gaussian random fields to model computer simulators. Gaussian process models are trained on input-output data obtained from simulation runs at various input values. Following this approach, we propose a sequential design algorithm, MICE (Mutual Information for Computer Experiments), that adaptively selects the input values at which to run the computer simulator, in order to maximize the expected information gain (mutual information) over the input space. The superior computational efficiency of the MICE algorithm compared to other algorithms is demonstrated by test functions, and a tsunami simulator with overall gains of up to 20% in that case.