scholarly journals Multi-scale membrane process optimization with high-fidelity ion transport models through machine learning

2020 ◽  
Author(s):  
Matthias Wessling
Keyword(s):  
Global Optimization ◽  
Ion Transport ◽  
Transport Model ◽  
Membrane Module ◽  
Process Models ◽  
Plant Design ◽  
Deterministic Global Optimization ◽  
Transport Models ◽  
Multi Scale ◽  
Process Plants

Innovative membrane technologies optimally integrated into large separation process plants are essential for economical water treatment and disposal. However, the mass transport through membranes is commonly described by nonlinear differential-algebraic mechanistic models at the nano-scale, while the process and its economics range up to large-scale. Thus, the optimal design of membranes in process plants requires decision making across multiple scales, which is not tractable using standard tools. In this work, we embed artificial neural networks (ANNs) as surrogate models in the deterministic global optimization to bridge the gap of scales. This methodology allows for deterministic global optimization of membrane processes with accurate transport models – avoiding the utilization of inaccurate approximations through heuristics or short-cut models. The ANNs are trained based on data generated by a one-dimensional extended Nernst-Planck ion transport model and extended to a more accurate two-dimensional distribution of the membrane module, that captures the filtration-related decreasing retention of salt. We simultaneously design the membrane and plant layout yielding optimal membrane module synthesis properties along with the optimal plant design for multiple objectives, feed concentrations, filtration stages, and salt mixtures. The developed process models and the optimization solver are available open-source, enabling computational resource-efficient multi-scale optimization in membrane science.

scholarly journals Multi-scale membrane process optimization with high-fidelity ion transport models through machine learning

2020 ◽  
Vol 608 ◽  
pp. 118208 ◽  
Author(s):  
Deniz Rall ◽  
Artur M. Schweidtmann ◽  
Maximilian Kruse ◽  
Elizaveta Evdochenko ◽  
Alexander Mitsos ◽  
...  
Keyword(s):  
Machine Learning ◽  
Ion Transport ◽  
Process Optimization ◽  
High Fidelity ◽  
Membrane Process ◽  
Transport Models ◽  
Multi Scale

scholarly journals Deterministic global optimization with Gaussian processes embedded

2021 ◽  
Author(s):  
Artur M. Schweidtmann ◽  
Dominik Bongartz ◽  
Daniel Grothe ◽  
Tim Kerkenhoff ◽  
Xiaopeng Lin ◽  
...  
Keyword(s):  
Global Optimization ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Optimization Problems ◽  
Process Models ◽  
Bayesian Optimization ◽  
Computational Time ◽  
Chance Constrained Programming ◽  
Deterministic Global Optimization ◽  
Gaussian Process Models

AbstractGaussian processes (Kriging) are interpolating data-driven models that are frequently applied in various disciplines. Often, Gaussian processes are trained on datasets and are subsequently embedded as surrogate models in optimization problems. These optimization problems are nonconvex and global optimization is desired. However, previous literature observed computational burdens limiting deterministic global optimization to Gaussian processes trained on few data points. We propose a reduced-space formulation for deterministic global optimization with trained Gaussian processes embedded. For optimization, the branch-and-bound solver branches only on the free variables and McCormick relaxations are propagated through explicit Gaussian process models. The approach also leads to significantly smaller and computationally cheaper subproblems for lower and upper bounding. To further accelerate convergence, we derive envelopes of common covariance functions for GPs and tight relaxations of acquisition functions used in Bayesian optimization including expected improvement, probability of improvement, and lower confidence bound. In total, we reduce computational time by orders of magnitude compared to state-of-the-art methods, thus overcoming previous computational burdens. We demonstrate the performance and scaling of the proposed method and apply it to Bayesian optimization with global optimization of the acquisition function and chance-constrained programming. The Gaussian process models, acquisition functions, and training scripts are available open-source within the “MeLOn—MachineLearning Models for Optimization” toolbox (https://git.rwth-aachen.de/avt.svt/public/MeLOn).

On Global Feasible Search for Global Design Optimization With Application to Generalized Polynomial Models

1992 ◽  
Author(s):  
Chihsiung Lo ◽  
Panos Y. Papalambros
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Model Transformation ◽  
Special Problem ◽  
Search Algorithms ◽  
Deterministic Global Optimization ◽  
Generalized Polynomial ◽  
Polynomial Models ◽  
Feasible Solutions ◽  
Global Design Optimization

Abstract A powerful idea for deterministic global optimization is the use of global feasible search, namely, algorithms that guarantee finding feasible solutions of nonconvex problems or prove that none exists. In this article, a set of conditions for global feasible search algorithms is established. The utility of these conditions is demonstrated on two algorithms that solve special problem classes globally. Also, a new model transformation is shown to convert a generalized polynomial problem into one of the special classes above. A flywheel design example illustrates the approach. A sequel article provides further computational details and design examples.

The effect of the pool and riffle on dissolved, non-conservative mass transport in rivers

2013 ◽  
Vol 48 (3) ◽  
pp. 232-242
Author(s):  
Ian H. Halket ◽  
Peter F. Rasmussen ◽  
John C. Doering
Keyword(s):  
Transport Model ◽  
Low Flow ◽  
Transport Models ◽  
Cross Sectional ◽  
Lower Velocity ◽  
Regulatory Limits ◽  
Uniform Channel ◽  
River Reach ◽  
Model Equations ◽  
Sectional Shape

One-dimensional substance transport models assume that the river reach modelled has a uniform cross-sectional shape which manifests as a constant average velocity in the model equations. Rarely do rivers meet this criterion. Their channels are seldom uniform in shape but rather alternate in a quasi-periodic manner between pool and riffle sections. This bedform sequencing imparts a corresponding variation in the average cross-sectional velocity which is not accounted for in constant velocity transport models. The literature points out that the pool and riffle planform may be the reason for the sometimes poor predictions obtained from these models. This paper presents a new variable velocity transport model and confirms that the fluctuation in average cross-sectional velocity caused by the pool and riffle planform does have a marked effect on transport in rivers. The pool and riffle planform promotes an enhanced decay of a substance when a first-order biochemical reaction is simulated with the new transport equation. Investigation of the analytical solution shows that the enhanced decay is the result of the overall lower velocity experienced in a pool and riffle channel as opposed to a uniform channel. This difference in transport velocity between a pool and riffle channel and a uniform channel becomes more pronounced as flow declines a critical finding for total maximum daily load calculations because these regulatory limits are usually determined for low flow levels by models that do not account for this phenomenon.

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