Ivo Couckuyt

Multi-objective geometry optimization of a gas cyclone using triple-fidelity co-kriging surrogate models

Cyclone separators are widely used in a variety of industrial applications. A low-mass loading gas cyclone is characterized by two performance parameters, namely the Euler and Stokes numbers. These parameters are highly sensitive to the geometrical design parameters defining the cyclone. Optimizing the cyclone geometry therefore is a complex problem. Testing a large number of cyclone geometries is impractical due to time constraints. Experimental data and even computational fluid dynamics simulations are time-consuming to perform, with a single simulation or experiment taking several weeks. Simpler analytical models are therefore often used to expedite the design process. However, this comes at the cost of model accuracy. Existing techniques used for cyclone shape optimization in literature do not take multiple fidelities into account. This work combines cheap-to-evaluate well-known mathematical models of cyclones, available data from computational fluid dynamics simulations and experimental data to build a triple-fidelity recursive co-Kriging model. This model can be used as a surrogate with a multi-objective optimization algorithm to identify a Pareto set of a finite number of solutions. The proposed scheme is applied to optimize the cyclone geometry, parametrized by seven design variables.

A Kriging and stochastic collocation ensemble for uncertainty quantification in engineering applications

We propose a new surrogate modeling approach by combining two non-intrusive techniques: Kriging and Stochastic Collocation. The proposed method relies on building a sufficiently accurate Stochastic Collocation model which acts as a basis to construct a Kriging model on the residuals, to combine the accuracy and efficiency of Stochastic Collocation methods in describing stochastic quantities with the flexibility and modeling power of Kriging-based approaches. We investigate and compare performance of the proposed approach with state-of-art techniques over benchmark problems and practical engineering examples on various experimental designs.

Gaussian Processes for history-matching: application to an unconventional gas reservoir

The process of reservoir history-matching is a costly task. Many available history-matching algorithms either fail to perform such a task or they require a large number of simulation runs. To overcome such struggles, we apply the Gaussian Process (GP) modeling technique to approximate the costly objective functions and to expedite finding the global optima. A GP model is a proxy, which is employed to model the input-output relationships by assuming a multi-Gaussian distribution on the output values. An infill criterion is used in conjunction with a GP model to help sequentially add the samples with potentially lower outputs. The IC fault model is used to compare the efficiency of GP-based optimization method with other typical optimization methods for minimizing the objective function. In this paper, we present the applicability of using a GP modeling approach for reservoir history-matching problems, which is exemplified by numerical analysis of production data from a horizontal multi-stage fractured tight gas condensate well. The results for the case that is studied here show a quick convergence to the lowest objective values in less than 100 simulations for this 20-dimensional problem. This amounts to an almost 10 times faster performance compared to the Differential Evolution (DE) algorithm that is also known to be a powerful optimization technique. The sensitivities are conducted to explain the performance of the GP-based optimization technique with various correlation functions.

Random Survival Forests for Predicting the Bed Occupancy in the Intensive Care Unit

Predicting the bed occupancy of an intensive care unit (ICU) is a daunting task. The uncertainty associated with the prognosis of critically ill patients and the random arrival of new patients can lead to capacity problems and the need for reactive measures. In this paper, we work towards a predictive model based on Random Survival Forests which can assist physicians in estimating the bed occupancy. As input data, we make use of the Sequential Organ Failure Assessment (SOFA) score collected and calculated from 4098 patients at two ICU units of Ghent University Hospital over a time period of four years. We compare the performance of our system with a baseline performance and a standard Random Forest regression approach. Our results indicate that Random Survival Forests can effectively be used to assist in the occupancy prediction problem. Furthermore, we show that a group based approach, such as Random Survival Forests, performs better compared to a setting in which the length of stay of a patient is individually assessed.

Efficient Multi-Objective History-Matching Using Gaussian Processes

In a multiobjective optimization approach, a trade-off is sought to balance between the optimality of different objectives. In this paper, we introduce a new efficient multiobjective optimization approach using sequential Gaussian Process (GP) modeling that can quickly find the Pareto solutions in a minimal number of model evaluations. This is the first time that we present this approach for history-matching. The difference with other optimization algorithms is elucidated for the cases where we can only afford to run a limited number of simulations. Unlike other surrogate-based methods, we do not aim for a greedy approach by minimizing the surface itself as there can be a large uncertainty in the surrogate approximations. Instead, statistical criteria are introduced to account for both proxy model uncertainty as well as its extrema. This multiobjective optimization approach has been successfully applied for the first time to history match the production data (i.e. pressure, water and hydrocarbon rates) from a multi-fractured horizontal well in a tight formation. A GP surface is constructed for each misfit, to provide the predictions and the associated uncertainty for any unknown location. Multiobjective criteria, i.e., the hypervolume-based Probability of Improvement (PoI) and Expected Improvement (EI), are developed to account for the uncertainty of the misfit surfaces. The maximization of these statistical criteria ensures to balance between exploration and exploitation, even in higher dimensions. As such, a new point is selected whose values in different objectives are predicted to hopefully extend or dominate the solutions in the current Pareto set.

Multi-objective optimization of reflector antennas using kriging and probability of improvement

This paper presents the multi-objective optimization design of a blocked prime focus reflector system using a Kriging response surface approximation technique with adaptive sampling. Samples are added to the model by selecting those with the highest probability of improving the current estimate of the Pareto front. The problem is especially difficult due to the multi-modal nature of the Pareto front, and a good estimate is achieved using only a modest number of full wave simulations.

Surrogate modeling with sequential design for design and analysis of electronic systems

The growing computational demands of modern engineering simulations as used frequently in fields ranging from computational fluid dynamics to electromagnetics, requires methodologies to be able to perform evaluation intensive tasks. Popular analyses include design space exploration, visualization, optimization or sensitivity analysis. This work provides an overview of advancements in surrogate modeling, a data-driven approximation technique. Both sequential design and adaptive modeling are covered, and an integrated platform for surrogate modeling is presented. Finally, a recent technique known as deep Gaussian processes is highlighted as a promising alternative for surrogate modeling of non-stationary response surfaces.

An Adaptive Sampling Strategy to Accelerate Markov Chains Monte Carlo

Markov chain Monte Carlo (McMC) is a technique to sample the posterior distributions in order to quantify the uncertainty and update our knowledge about the model parameters. However, this technique is computationally costly. Therefore, it is frequently combined with a cheap-to-evaluate proxy model. Building an efficient and accurate proxy model using one-shot sampling method (such as Latin-Hypercube) is a challenging task as we do not know a prior the best sample locations and the number of required samples to tune our proxy model. In this paper, we present a novel adaptive sampling techniques using LOLA-Voronoi and Expected Improvement techniques to sequentially update our proxy (here ordinary Kriging model) using best sampling locations and density. This algorithm is used to balance between the exploration and exploitation to create an accurate proxy model for the IC fault model’s misfit function. The results show a large improvement comparing to the one-shot Latin-Hypercube design. The built proxy is then employed to reduce the computational cost of McMC process to find the posterior distributions of the model parameters.